TL;DR: because they can delete everything.
By employer’s email account I mean something like
I recently parted ways with my previous employer. It all went super smoothly and my previous employer was nothing but super nice and compassionate. However, after a while, they naturally shut down my email account. And I was so close to losing some important documents like contracts, hardware receipts, promotion agreements, and such. Luckily I had a copy of everything on my email client and I could save a backup. But it made me realize that my employer had absolute power over my account all along. I trust my previous employer with this power, they’re great people, but why trust when you can know?
Obviously, it is normal to use the company’s email for work-related communication, but when it comes to negotiating your very contract, the counterparty shouldn’t have access to deleting your side of the argument. Use your personal email when negotiating your salary, contract, or whatever unshared interest with your employer.
This is especially relevant for remote workers where contracts and negotiations are mostly digital.