Two things here.
- GDPR does not allow users to modify their data at all costs. There is a legitimate interest for the forum owner as well.
- GDPR doesn’t require that users can do this in an automated way. So if you really have a problem with a like that you have given, you could also email or PM the admin / moderator and ask them to remove it.
GDPR is not a generic get-out-of-jail-for-free card.
For forums one could argue that article 17.3 of the GDPR applies:
Paragraphs 1 and 2 shall not apply to the extent that processing is necessary:
(a) for exercising the right of freedom of expression and information;