If you are currently underpaid (and many people early in their careers are), this is a way to keep being underpaid.
What if they are willing to offer 50% more, but you ask for 20% more and end up with it?
If they go first, and they lowball you, you can always ask for more. If you go first and say "I want $X", and they say "OK!" you probably left money on the table.
You have a lot of experience, so you probably know what you are worth. But a lot of people a few years into their careers would undervalue themselves in this kind of negotiation if they went first, especially if they are transitioning from startups to big tech.