I actually feel 'that' sounds more natural to me in this text, as 'the point' represents an abstract idea/concept, not a physical location. I'd definitely say 'that' in this example, anyway.

The context talks about "feeling trapped" which suggests a physical location. "where" sounds good to me because of that. However, "that" certainly doesn't sound bad or wrong.

What your lecturer said seems right to me. In your example "point" is a place (albeit a metaphorical place). You could think of this as "...it gets to the place... WHERE all that matters..." I hope that a professional teach weighs in on your question, because I really don't know the grammatical rules that govern this, and I'd be interested to know the definitive answer myself.

@Michael Smith Thank you very much for your answer and the life tip

It's a very pedantic teaching point. Some lecturers are like that. I think he's wrong, too. See https://www.englishgrammar.org/that-instead-of-when-and-where/ On google today, "it's come to the point that" is about four times more common than "it's come to the point when" - and "it's come to the point where" is about used about one and a quarter times as often as "it's come to the point that". Not that that proves anything. But she or he is still your lecturer, so for the purposes of a quiet life and a good mark it's probably better to comply, in class at least :)