Are you a native of Gaelic/advanced speaker? Just so I know from what experience you're speaking :P Languages often don't behave obviously or intuitively, particularly according to the logic followed by other languages that often form learner biases—hence why I'm asking rather than forming my own conclusion based on what seems to make sense from my point of view.
Because there's too many verbs in that sentence. Agam and orm both fill the same function so you can use one or the other. "Chan eil brog agam" means "I have no shoe" and "Chan eil brog orm" means "I wear no shoe". (I changed it to a slightly awkward sentence structure there so that you can see the similarity better). You wouldn't say "I wear have no shoe". It's just not done.
I can't be sure how new you are to language learning, so apologies if this seems too condescending - I really don't mean it that way. But it occurs to me that you might be thinking you ought to literally translate "have on" as a two word construction so that's why you're thinking have/agam + on/orm. But that's not how languages work. It's not like a codebook where you just swap out words to get the answer. Gaidhlig uses a completely different sentence structure and many words won't translate nearly on a one-to-one basis.
In English, "have on" is effectively a compound verb (technically a verb phrase). In Gaidhlig "orm" is a single word verb that fulfills almost the same function. (It's actually slightly more because the m at the end indicates "me/I" so it's conveying more "I have on"). So there's no need to put a separate "have" into the sentence.