Why do western governments take in so many immigrants?

[JimBeam]

It all started with the brain drain, Germany offered education to professionals from the Middle-East and sub-saharan Africa and convinced the best engineers etc who also learned the language to stay there, also France did the same from it's former colonies.
So the people who could actually contribute to those countries actually never went back, therefore the economics opportunities in Africa is basically zero, apart from exploiting it's vast natural resources.

A popualtion boom happened in Africa and after the Arab Spring made by the nice Americans the road to Europe was cleared.

Getting educated engineers is one thing but letting random people without any checks into the country is madness.

Merkel thought these new migrants will want to study and work just like the 1st wave, but 94% of them just wants to use the social benefits and has no plan to work. Saudi-Arabia even built city quarters for them but no migrants going there because again they don't want to work.

Exactly. Most of them don't want to work. And also don't want to change and integrate.

Hungary tries to solve it's demographics issues with different methods, give couples many benefits who will have kids, import workers from Vietnam and the Philippines. I'm not sure if it will work but certainly sounds more appealing than letting millions of muslims in.
I'm biased but if I were living in Western-Europe I would certainly move to Hungary or Poland if I still want to live in the civilized Europe in the future.

Well, this Hungarian thing is actually having some results. The fertility rate has increased in the past years but it's still far from good but the uptrend is a good sign. Things like that take time.
The questions that remain are: is the growth good enough so economy won't get hurt or they'll still need to import some workers to get things done and are the people staying in Hungary or trying to find better life in Austria, Germany or Switzerland.

I'm not a fan of the authoritarian leaders like Victor Orban and Putin, but when they sound more reasonable than the US president, you know there is something wrong.

Being more reasonable than the old guy is not difficult.