I can’t quite answer the why but it is right here in Jisho. This is the only way it exists in any E-J dictionary I have, and the same goes for 大辞林, 出づる isn’t in any of them.
I wrote up a big guess as to why this is, but then I found the actual answer. The actual verb here is the old 二段 verb, 出づ (いづ). This is a verb on its own, the る is redundant, but you may also notice there are no verbs in modern Japanese that end in づ or ず (which it would be written as today). All 二段 verbs changed in 一段 verbs, with one exception that is irrelevant to this discussion, and so appear to have gained an る, this means that the verb いづ became the modern 出る we all know and love.
So, with that said, 出づる is some kind of “Half-breed”, in that it sounds “old” but it is still using modern orthography. The second answer here suggests that this comes from the reforms made with the New Kana usages they said, "There is no need to obey the rules of 文語 when writing with modern Kana. So you put the る on the end there. But, that does mean it will not exist in most dictionaries. I’m not even sure if it’d be in the 広辞苑