(and I really am not interested in what your "instructor" said - if he told you that he's an idiot)
Progress in science is not based on wishful thinking - it's based on accumulating facts by long hard struggle.
One of those facts is - given the simplest assumptions about space and time - assumptions taken from the simplest observations about the world - then space and time are related by a parameter that is either finite or not - and the only way to find out which, is to look. When you look, it turns out to be finite. There is no doubt, none whatsoever - about this. NO DOUBT. It is as real as rain.
Not you, not anyone or any thing, will ever go faster than this limiting speed. And if you insist on believing that it will, then you are rejecting science and its methods, and you should not pay lip service to it ever again. You should crawl up a tree and live like the monkeys do, without science.