A lot of small startups don't have a mat/pat policy yet, maybe not a well developed vacation policy either nor a generous one, and the employment may be "at will" meaning they can let you go for no reason, just because they decide "why keep paying?" I know there are exceptions in law for parental reasons, but whether they apply depends on the type of contract.

On top of that, the startup may find it difficult to pay someone else while still paying you. If you're an early employee, there may also be financial incentives to the company letting you go, such as not having to pay out the higher rate or higher equity you negotiated as an early joiner.

You can take the time off but in some cases are risking losing your job by doing so for long. If you need the money, that's a tought spot. Even if you're good at getting new jobs (many people aren't), getting a new job can be a full time job in itself which you don't have time to do if you're seriously on mat/pat, and anyway few companies will hire you while you're still unavailable.