Oh, I see. Well, the verb is szület (to be born), & I think you never lose vowel through conjugation of verbs (if someone knows of a counterexample, please tell me.) So you need to put the -t of the past tense to szület, but you have to inject a connecting vowel here (-e-, in this case.) The -t of the past tense becomes -tt before vowels, so what you get is született.
Forog, forgott. I think the reason for these may be that there is a deeper root of the word. Here, "for-". The root is not a word in itself (maybe it never was), we can only see it from other derivatives, like "fordul", etc. So, "-og" is some kind of suffix that we can see in other words, as well.
"Fürödni" is a bit tricky because it also exists in the "fürdeni" form, so it could be argued that various forms are used for various persons. I am not sure. It is also an "-ik" verb, which is tricky enough.
With "születni", if we left out the "e", there would be too many "t" sounds in one group. Plus, it would be too close to some conjugated form of "szülni". And, anyway, the "-at"/"-et" suffixes probably never lose their vowels.
I think dropping vowels is more of an exception. Those are the special ones.