You're basically walking into the middle of a niche debate about semantics. There is a faction that dislikes the use of the word "anthropocene" to refer to the current geological era - and specifically, the past 100 years or so. Their main argument is that it's an imperceptible blip on the radar compared to the scale of other geological eras we study.

This article is a response that can be summed up as "no, we're changing the environment faster than anything before, so it counts". It's framed not as a genuine debate, but as an attempt to dispel "myths".

"Why this matters" is left as an exercise for the reader...

Scroll halfway down to find a numbered list, with headings. Personally, I couldn't simplify it anymore than that.