There are several possible reasons why your Neopet is unable to wear an item of clothing in your closet.
The item may already be worn by another one of your Neopets. Remember to click the "save" button after you have finished adding or removing items!
Not all wearable items can be worn on all species of Neopets, however! You'll never be able to convince your kacheek to wear a Moehog Flapper Dress, for instance. Species specific wearables will usually have the Neopet that can wear them in the item name.
Some wearable clothing items cannot be applied to unconverted Neopets or the following painted Neopet body types: Maraquan, mutant, baby, invisible, and fruit and vegetable Chias unless specified in item details. Some Premium items may only be wearable with specific painted Neopet body types such as baby.
Finally, your clothing item may be saved as a "preset" on one of your other Neopets!