Why do many people equate schizophrenia with multiple personalities?

Possibly because when a schizophrenic acts out the instructions of the voices he or she hears, they act in a manner not considered their usual, making people think they have another personality inside them. If they respond verbally, and are overheard, the listener may be confused about what they suffer from. And Multiple personality Disorder does exist, but it is very rare. We usually find easier ways to cope with our problems.

me....................me......... me! signed, Jim
Because most people do not understand mental health disorders. And since schizophrenia has sometimes been called "the split mind" people assume that means more than one personality.

That is why they changed the Multiple Personality Disorder to Dissociative Identity Disorder, to clear up that confusion about "a split mind."
Multiple personality does not exist
Primarily, the confusion arises from misinformation and ignorance.

Also, as more research advancements are made, and further information is available, the psychiatric community and the DSM continue to change the terminology of many mental illnesses, which can make it difficult to keep one disorder separate from another over the years.

Unfortunately, movies and bad television have also served to negatively further the cause of total confusion as to what exactly schizophrenia is.

My heart truly goes out to those who actually suffer from schizophrenia. I'm sure THEY know what it really is. Much like those afflicted with Tourette's Syndrome know that their condition is much more than just shouting out random profanity, as it's usually portrayed onscreen.
The answer is that the latin root of the word schizophrenia literally translates to "split mind."
Also, miseducation leads the general public to only think of one mental disorder (schizophrenia) with one group of symptoms (MPD).