Evolutionists confidently assert that dinosaurs are millions of years old, and all died out 65 million years ago. But how do they know this? How do you know when dinosaurs evolved and when they went extinct? The fact is, you can't. It's a religious story, not a scientific fact.
If you want to know how old something is, you usually have to check some records. But no fossil has ever been unearthed with such records. While there are some very shaky dating methods Evolutionists use to say dinosaurs are millions of years old, there are several things that exist that strongly suggest they are not.
For example, it is not uncommon to find soft tissue in dinosaur remains. Most famous among such discoveries is Mary Schweitzer's t-rex, in which she found stretchy blood vessels. In Schweitzer's own words, "It was exactly like looking at a slice of modern bone." (1) Given that Schweitzer remains an Evolutionist to this day (as far as I know), one can hardly shrug this off as "sloppy" Creationist science. But of course, Schweitzer was still mocked for this, because Evolution doesn't typically yield to evidence.
Another example comes from a presentation at the Western Pacific Geophysics Meeting in Singapore, in which the researchers showed that they had carbon dated samples from 8 dinosaur specimens to roughly 22,000 to 39,000 years old. The fact that there is any Carbon 14 in dinosaur bones is impossible if they are millions of years old, so even with the extremely high age of 22,000 years old, that's way too young if the Evolutionary narrative is to be believed. These findings are so damning to Evolution that they were intentionally (and secretly) removed from the conference website by chairmen Minhan Dai and Peter Swart (2), simply because two chairmen refused to accept them.
If the evidence renders the narrative unbelievable, it makes sense to not believe it. The evidence fits much better with the Biblical history of the Earth: God made dinosaurs with man (Genesis 1:24-27), and then, sadly, man outlived the dinosaurs.
References
1. Schweitzer, Mary - Montana State University Museum of the Rockies; cited on p. 160 of V. Morell, ‘Dino DNA: The hunt and the hype’, Science 261(5118):160–162, 9 July 1993
2. Fischer, John Michael - Carbon-14-dated dinosaur bones are less than 40,000 years old. New Geology (link)