I’m just saying young people believe in climate science

If you actually want to understand why you got push back then that's not actually what you said, or implied. Your wording was a rebuttal of the statement that average older people have personally observed the pattern of climate changing. Young people believing in climate science at a higher rate than older people can also be true and is not contradictory.

The point you seem to have missed is the older people should not need to "believe" - they have literally experienced the change and should be able to observe the pattern and draw a logical conclusion.

The problem you are raising is real, but it's a totally different one - the impact of propaganda and rationalising something that isn't true. When you talk to your parents get them to talk about when they were kids, ask them what winters were like, the example in thread about Halloween is a great one - get them talking about trick or treating as a kid, was it cold etc then you can gently point out that it wasn't like that for you (if that example doesn't work pick another).

The point though is your parents are wilfully ignoring the evidence of their own senses most likely because Fox news and their conservative friends told them to, and that social pressure is greater than logic.