Often the severance is offered alongside an agreement not to sue the company for anything, not to disparage, etc, and you only get the severance if you agree to the contract.
It can be a negotiation, you can tell them you will decline the severance and hold onto your ability to sue and disparage, and see if their offer increases, or see if you can adjust the terms of the agreement, etc.
This is a big reason why you rarely hear bad things about working at BigCo, at least not specific stories in the media about specific people that were perfectly competent but just lost out to the political process, any any such complaints are just vague, anonymous, unverifiable mumblings on forums.