To start with the obvious, this is setting a precedent, hence the plural (as in "these people").To start with the obvious we are talking about an individual, not these people.
A single teenage mother, not an ISIS fighter. Its not a matter of letting these people in, its a matter of does she have the right to return to the only country she has citizenship of and was born in.
The EU doesn't and won't recognise ISIS for obvious reasons.
1-2. I imagine that joining ISIS at the very least makes her a supporter of terrorism. I'm not a lawyer, but I believe that's against UK law1. This power was introduced to be used against dangerous terrorists. There is no evidence of her committing any terrorist acts.
2. Since its introduction the Home Secretary has expanded its scope to include people who commit grave criminal offences. There is no evidence of her having committed any.
3. We are committed to not making people stateless. She has no other nationality.
4. Its a bad law because it gives a quasi-judicial power to a politician and appeals against his decision are made by a commision that hears evidence in secret which the person appealing has no access to so can't dispute.
5. Why should I or she have to make a case? The Home Secretary has not shown her to be a threat to national security. It is hard to imagine her as one.
3. She is a member of the Islamic state. If the Islamic state failed to issue her a passport, then I'm going to go with "not my problem"
4. If you want to change the process, perhaps there is a case to be made for it. But right now, we can only use the laws we have. Perhaps I'm only speaking for myself, but this is not a person I'd want in my country
5. Joining and supporting ISIS makes her a threat to national security