The “burning IVF clinic” is a poor instance of analogous reasoning. The reasons why one would save a 5-year old, are not fundamental moral principles but purely psychological. One would save friends or attractive people first as well, this does not grant them greater moral value.
Even if we don’t consider it to be purely emotional preference, the “triage” rebuttal can hold as well. I.e the fact that we choose a 5-year old is that their value is more immediately apparent, even if we have no reason to believe them to be more morally valuable.
“You don’t believe that it isn’t”
The problem here is that if you want to show that something is true, you can’t rely on premises being true that require the conclusion to be true. It just becomes a useless tautology that provided no additional information.