> If you are British at birth they can't strip your citizenship and kick you out

Not true. If you have dual nationality at birth, typically because you have one British parent and are born in the UK, then you are British at birth but the Home Secretary has the power to strip you of British citizenship anyway.

So, paradoxically, a child born in the UK to a British mother can end up with stronger UK citizenship rights if the mother doesn't reveal who the father is.

That's not as bad as if you are a naturalized British citizen. In that case, the Home Secretary has the power to strip you of British citzenship and leave you entirely stateless (you have no citizenship anywhere), which you can imagine is a very difficult status to live with.