And you depend on doctors and sewerage workers and programmers and garbage men and police officers and soldiers and physicists and so on. Is it selfish not to become all of these things yourself?

As long as you participate actively in society by working, you are doing your part and are not being selfish.

And my taxes go towards (in most countries) supporting that. Also, the children are not obligated to take care of me. They can choose it as a profession and I will gladly pay them for it, just as I gladly pay any professional in my life for cutting my hair or helping my children if they have trouble at school (even though they themselves do not have to have children and are helping them instead of the other way around). Are the people providing services also selfish for providing them?

Why? Anyone paying taxes to the state has fully earned their right to exist, especially if the state has a welfare system.

Not having children isn't even a new concept. People have done it since time immemorial. What if they had multiple children and then lost them all to the statistically high child mortality rates? Were they being selfish by not furthering their lineage due to external circumstances?