Is it possible for people who don't like math to become a good programmer?

No, no-no, no, yes and no!

No, because often you need it.

(! (a | (! (b && c) || d) && (! e)))

Why doesn't it work?

foo ('a', 'b', 19, g(h))
bar ('c', 'd', 44) 

can it be rewritten in a more abstract way?

Is 968 ms more or less than 0.7 s? How many MB do you need, how many Ghz does the machine have, will a byte be enough - math is everyday part of the job. Sometimes explicitly and higher math.

Always implicitly lower math.

Math is a wide field, from calculating, to matrix, to geometry, logic, statistic, category theory, graph theory. So if you believe you're programming without using math - maybe you're wrong.

If you look at problems at the Project Euler page, you will find puzzles, where I don't have an idea, how math is used to solve it. (Not that I could solve them without math.) Note that the problem size is normally that big, that you can't solve them with brute force.

However - since I can't solve lot of them (about 2/3 by now), does it mean that I don't like math?

If you didn't study math, you will probably not know, where you can find math your daily life, including programming.

Even if you just specialised in moving GUI-components on the screen to look good, you're doing math in some way.