Thanos is just buying into neo-malthusian rhetoric. No, overpopulation is really not a problem. Overcrowding, maybe, and definitely overconsumption, but the issue is not that there are too many people - the issue is city design and a system in which we are encourage to consume far, far, far too much. The solution to the problem of overconsumption being the murder of half of all populations is completely fucked up.
The book for his origins goes into this a bit more.
Thanos's father was working on new buildings and slef sustaining towers for people to live in, that would help with the overpopulation. But the construction of those was going to be to slow and the resources needed for it would cause ecological harm that would decimate the planet. It's essentially us needing to produce greenhouse gases to mine material for batteries, with that greenhouse gas emissions causing severe storms and weather that would destroy whatever self sustaining resources we would have. Thanos ran all the possibilities, and deduced that population reduction and time for the planet to heal was the only outcome. When he returned to his planet, everything he predicted in his calculations had come to pass, and the inhabitants tried every method to save themselves from ecological destruction.
He then went on a crusade, stopping other planets from having the same fate and ultimately deduced the rate the universe itself would run out of habitable resources, and decided that it was better to kill half of everything now and kill trillions, rather than hundreds of trillions all dying hundreds of thousands of years from now.
The problem with Thanos is he doesn't understand the value of life, his entire upbringing was in near isolation and he was scorned from society. The empathy most people have, he never grew up with due to his father and his planets distaste for him since he had several genetic mutations.
The story with Thanos works because he is making a decision that if happened today, would save our planet from severe ecological destruction and a snap would effectively bring our CO2 emissions under control. We're all in the family car ready to drive off a cliff, but because we have human connection and are emotional, we'd never kill those who know how to drive to prevent it. Thanos see's the people as simple numbers, unlike every other living being he doesn't see the importance of each person or what they mean to other people.
It's an impossible choice, if you were told you had to kill half your family so the rest of your family could live, could anyone be able to pull the trigger on that? No. But he sees himself capable of making the sacrifice of making that choice for everyone and being able to take the burden away from them.