As the others said - XSS. Stored XSS can still be a vulnerability with secure cookies, but locally stored tokens are a dramatically easier thing to take advantage of as an attacker, as they can just exfiltrate the token and hit your APIs with it.
For web browsers, cookie-based auth solves a ton of browser-specific problems that history has spent a long time building up answers for.
For web browsers, cookie-based auth solves a ton of browser-specific problems that history has spent a long time building up answers for.