I have often heard this "argument" that science is something that we just chose to believe;
Punch them in the face. Hard. Explain that you reject the scientific evidence for the assumption that this would hurt or injure them rather than see your point of view.
and it's just as much of a faith as religion. I'm sure you've heard it too. How do you deal with it?
Right, so may I don't punch people in the face. But if someone outright rejects rationality, it's usually fairly pointless to continue talking to them...
I get so annoyed at that "argument" that I usually get rude and sarcastic. But I wanted to know how I can counter that without being sarcastic.
Boy, I'm really not the right person to answer this. I would suggest a long list of scientific facts that they belief and rely or benefit from.
Ask them why they are not chained to the ground and why they chose to belive that Gravity isn't going to fail any moment now.
Or take the boring route: Explain what science is and how it works. (I'm sure you will find threads here discussing that very question.) Explain to them that there is no question about believing something after the evidence is in. Relying on Gravity is not wishful thinking!
How can I construct a reasoned argument against that? Should I start from how axioms in maths and science are self-evident truths and belief in them is not even remotely close to belief in a religion.
Any help would be greatly appreciated.
This is not really my field, so I'm certain others will correct me ...
axioms in math are not self evident, they are defined to be true. They might not be. (And I think there are systems that use other axioms than the ones you and I are probably familiar with.)
Science is actually different from math and it shouldn't make any assumptions like that at all. Things in science are not self-evident. They are tested and proven.
It might be self evident that light moves like a straight particle beam - when experiemnts showed that this could not be so, however, that notion was modified.
I am not sure if it is much help to contrast science and religion - to me, they are two totally different things - not like apples and oranges but like tomatoe soup and a roller skate.