Why is this correct and the other not?

You can only invert certain verbs. dis-je, suis-je, ai-je for example but it iform and custom not something you can do with all verbs, that would be far too simple!

https://www.lawlessfrench.com/grammar/inversion/
Bonjour Kari,
This is a lesson written by Laura that explains the inversion a little more. Perhaps this will aid you somewhat.
Ron

Bonsoir Kari, Actually any verb can be used in inversion to form a question. If you read French literature, this is very common. In fact, inversion is considered by some to be a more formal structure. From the lesson: Simple Yes/No Questions The forms je peux, je vais, je suis, j'ai can be inverted but these forms are rarely used nowadays, as they're considered very formal and old-fashioned: Puis-je avoir le pain, s'il-vous-plaît? May I have the bread, please? Suis-je à la bonne adresse? Am I at the right address? Ai-je assez d'argent? Do I have enough money? Vais-je dans la bonne direction? Am I going the right way? Notice that je peux becomes irregular in the inverted form puis-je, probably to ease pronunciation. This structure is very formal as we stated before, so would only be used in polite contexts: the nearest English equivalent would be May I? Note also that although it's rare to invert Je + verb to make a question, it does happen with some verbs. I believe what Nicholas is referencing, if I may, is the inversion of first person, singular verbs using «Je», please see above. For the most part, most of the inversion verbs in literature that I run across do not use the first person, singular inversion. J'espère que cela vous aidera. Bonne chance, Ron

"Mets-je mes chaussures où d'habitude?" is incorrect because the "où" is in the wrong spot. You could say, "Où mets-je mes chaussures d'habitude?" and that would be just fine. When forming a question by inversion you put the interrogative pronoun in front of the sentence. Here are the three ways to ask this question for comparison: "Je mets mes chaussures où d'habitude?" "Où est-ce que je mets mes chaussures d'habitude?" "Où mets-je mes chaussures d'habitude?" Felitations amicales, -- Chris.