Babies are typically not aware that they are wearing a diaper as babies don't really know what a diaper is yet.
However as the baby grows into toddler age and begins talking then they can know that they are wearing a diaper once they figure out what it is.
And sometimes the toddler decides they either like to wear the diaper or they decide they hate wearing the diaper.
I've known some toddlers and even kids who loved to wear diapers and then some hated them.
I remember babysitting a 5 year old boy who was not potty trained and wore Luvs size 6 diapers all the time as he was not potty trained.
He refused to potty trained and would scream when you would try to put underwear on him.
He would instantly calm down when you put the Luvs diaper on him and he said he loved diapers and loved being wet.
So his mom said he could just stay in diapers and not fight it.
Babies take off their own diapers because they don't like the diaper or they have a rash or they just find it fun that they can take off the diaper and love seeing your reaction.
Toddlers sometimes hate wearing diapers and will take the diapers off.
In those cases you sometimes need to put some duct tape, packing tape, masking tape etc around the diaper waistband to keep the diaper on.
Or put hard to get off pajamas on your baby or toddler to prevent access to the diaper.
In some cases for toddlers taking off a diaper may be a sign of potty training readiness although that is not always the case.
Usually it's a case of the baby just going through a phase and having fun pulling off the diaper and eventually it will stop.
Imagine yourself being in a diaper and wetting it and pooping it and you too would likely want that off as well.
For most kids and babies wearing a diaper is not comfortable or fun for them.
Also some babies and toddlers just love being naked as well.