(Sorry, a long comment again ...)
I think Norbert described the issues accurately and fairly. This may be where if, particularly as an expat, you only watch the occasional clip from MSNBC or even CNN, or only follow the most 'progressive' Democrats, you may not get a very balanced picture.
Obama did indeed 'do it too' in the sense of deporting what were at the time record numbers of undocumented migrants. He's a lawyer and a constitutional scholar, and he knew that the executive branch of government is responsible for enforcing existing law. Hispanic groups were not happy with him over that, and for not pressing harder for immigration reform, in much the same way as African-American groups were not happy with him for not pressing harder on civil rights, sentencing reform, and other issues associated with what the right wing is all too quick to stigmatize as 'identity politics.' I hope the vehemence of the backlash has now opened their eyes a little to the reasons for his caution.
His administration did have a much more nuanced, and I would say at least somewhat kinder and gentler, approach to how they carried out that policy. They prioritized deporting people convicted of serious crimes, felonies as opposed to misdemeanors. (Although in the mix, they sometimes swept up people for 'crimes' that were pretty minor, like a young landscaping worker I met who had a friend deported for, IIRC, a first-time DWI offense. Young men, clubs, beer, not surprising. If citizen teenagers were thrown out of the country for DWI, rich parents everywhere would be up in arms.)
They didn't go after DACA kids, students, or members of the armed services. They didn't lurk around schools to arrest parents, or lurk at courts and arrest people who were doing the right thing by showing up for their court appointments, or lurk at workplaces and conduct mass raids that picked up people willy-nilly, whether they had extenuating circumstances like a clean criminal record or young children or not. They allowed many more people to remain in the community, often for years, while awaiting adjudication through the backlogged immigration courts. They tried to increase the number of immigration judges.
Border Patrol facilities, supervised by the horribly named 'Homeland Security' department, understandably don't have a mandate to provide more than minimal food, housing, and medical care. They're not supposed to have to keep people for weeks or months; the maximum is really supposed to be 72 hours.
Legally, that may be only for minors, per the Flores agreement which has recently been in the news. (The Trump administration has clearly violated it, and some of those cases even from a year or two ago are just now reaching the courts.)https://en.wikipedia.org/wiki/Reno_v._Floreshttps://www.justsecurity.org/61144/flores-agr...
But in practical terms, the places weren't designed to be detention centers, even for adults. The Trump administration has overburdened the Border Patrol by requiring them not only to detain more border crossers and separate more families, but also to house them for considerably longer periods of time, without the resources to do so. I have to agree with Norbert that it seems likely they welcome the PR effect of immigrants photographed in cages. It probably plays wonderfully to their base, which is what actually matters to them more than any actual deterrent effect.
The Obama administration was indeed quicker to move people out of detention centers, and especially to get migrant children and teens into shelters, which are at least supervised by (IIRC) Health and Human Services and often run by nonprofits. The Trump administration has belatedly tried to build a few more detention centers, but they can be left standing empty (as recently in far West Texas, I believe) when the flow of migrants suddenly slows again, as has apparently happened since the Mexican government made an agreement with the Trump administration to start cracking down on migrants rather than just letting them pass through.
I agree that it's sometimes a puzzle what drives these cycles, but I suspect there are actually connections between the Trump administration's policies in the US and the worsening situation in Central America. Ever since Jeff Sessions, the White House has been actively boasting about deporting a lot of Salvadorans and others whom they accuse, often on little evidence, of belonging to gangs. (And yes, the Obama administration was already focused on deporting those with criminal convictions, which undoubtedly included real gang members.) Even if the young men weren't gang members before, many of them will be after they get deported, because with the decline of sustainable agriculture on small rural farms (which is apparently partly a climate issue and partly one of consumerism, technology, and globalization), there are now so few jobs there for young men outside the gang economy, and so much pressure to join it.
So in essence, it may be those deportations of young single men, by whichever administration, that have caused more young families with small children, and teenagers who don't want to join gangs, to flee. Along with perhaps more instant publicization via social media of the US legal situation, with more migrants now supported by activist NGOs and aware that they have a legal right to claim asylum, even if they may not have a very strong case for it. It wouldn't even be surprising if anti-US hackers were also playing a role in amplifying that dialogue, realizing that the more problems we have on our own borders, the less inclined we may be to object when China, Russia, Turkey, etc. test the waters by pushing human-rights violations outward from their borders.
It just seems sad that we can't find space for migrants, even if they may be partly economic refugees, in some of the places in rural and inner-city America that evidently need young families to keep neighborhoods and small towns from falling into decay. The NY Times just had a rather sad article about how Bosnian refugees had once revitalized a part of the inner city of St. Louis, but have now largely left for the suburbs.https://www.nytimes.com/2019/08/18/us/bosnian...
On a tangent, here's another article, by the left-wing economist Paul Krugman, on German economic policy. The upshot is that he thinks negative interest rates are a sign that Germans are not doing enough to invest in things like infrastructure and stimulate the economy.True, Germany forced debt-troubled nations in southern Europe into punishing, society-destroying spending cuts; but it also imposed a lot of austerity on itself. Textbook economics says that governments should run deficits in times of high unemployment, but Germany basically eliminated its deficit in 2012, when euro area unemployment was more than 11 percent, and then began to run ever-growing surpluses.
Why is this a problem? Europe suffers from a chronic shortfall in private demand: Consumers and corporations don’t seem to want to spend enough to maintain full employment. The causes of this shortfall are the subject of a lot of debate, although the most likely culprit is demography: low fertility has left Europe with a declining number of adults in their prime working years, which translates into low demand for new housing, office buildings, and so on.https://www.nytimes.com/2019/08/19/opinion/tr...
There too, it seems that at least a modest influx of young, hard-working migrant families could actually be a beneficial stimulus, if they could only integrate well enough into existing small-town or inner-city life, and if projects like infrastructure, education, and health care could help create jobs. But I'm afraid that the decline of Christian religious communities in some of those same places, perhaps especially in the East where worship was discouraged, may only exacerbate the problem, leaving a social gap that is sometimes being filled only by racist groups with a pseudo-religious fervor.
There just are so many interlocking factors and consequences that have to be taken into account if you want to try to address any complex problem like international migration, from whatever angle. I just wish there were more people in the political realm who seemed genuinely interested in finding practical solutions.