I was reading through the metamorphoses and noticed that a fair amount of the myths have one of the characters being turned into either an object or an animal, examples being narcissis being changed into a flower and Io into a cow. Why was it that so many greek myths feature shapeshifting of some fashion? That is also to include the gods, who frequently change their form.
You're currently reading the metamorphoses, quite literally created to be a collection of stories concerning transformation. The title itself means "transformations". Not all Greco-roman (the metamorphoses isnt Greek) myths feature this type of change or shapeshifting.
That being said, the greeks and romans had a large number of aetiological myths, myths that explained why things are the way they are. Apollo and Daphne explains why Apollo took the Laurel tree as his patron plant, Narcissus and Echo explains why we have echoes and Narcissus flowers, and Arachne explains why spiders weave webs.
Transformation was often punitive, as the gods stripped someone of their humanity as punishment for a wrong doing, but it was also a romantic tactic, as ovid so clearly shows us.
The role of transformation and its perception in Greco-roman society isn't something anyone can say with absolutely authority, and I doubt you'll get a better answer than "because that was their belief system", but would be a cool thing to explore in a thesis
Most European cultures had/have a traditional belief that people could change into animals (or more rarely into plants) and that animals could transform into people. Modern people are most familiar with the story of the werewolf, a motif popularized in recent media, but the idea of these transformations is diverse, widespread, and apparently ancient. Because of the historical depth of this idea, it is predictable that one would find these sorts of transformations in ancient Greek literature.
This idea manifests in European folktales (stories told as entertaining fiction) but also in legends (narratives generally told to be believed). The transformation of people into swans, for example, is at the heart of many stories and manifests in ballet. Stories of mermaids, particularly those of the North Sea involving seal people, include the idea that these creatures can move back and forth between animal and human shape - at the heart of a widespread legend type. Medieval Scandinavian literature includes an echo of a belief that warriors could willingly transform - figuratively or literally - into bears or wolves.
The idea of transformation is so common in European folklore and historic literature that the only thing that would be surprising - and need explanation - would be if ancient Greek literature did NOT include this motif.