What about how there are infinite points on a line. Break a line in half: 1/2. Another half: 1/4. Then: 1/8, 1,16, 1/32, etc. The denominator amount has no limit. All of those intervals ACTUALLY EXIST on the line, so an infinite amount therefore exists in reality.

Infinity only becomes impossible when you try to define it as a definite value. Saying it doesn't exist because you never reach it is missing the point(!) of its notion.

Its a bit like saying tomorrow doesn't exist....because we never reach tomorrow. Infinity, like the concept of 'tomorrow' is a notion, not a definite value that you can see, or hold, or calculate.

I have a rule of thumb that anything which says "infinity" is not actually mathematics. This is because there are a large number of mostly-unrelated concepts of the infinite in mathematics, and an actual mathematical usage would distinguish which one was being referred to.