Mayonnaise has vinegar in it mostly as a preservative so it does not become susceptible to bacteria as easily as some other foods do. There are many other additives which are put into mayonnaise such as lemon juice which help to preserve and keep it from spoiling over time.
Although these additives can delay the growth of bacteria, if a jar on mayonnaise is left out long enough past the expiration date it can develop salmonella bacteria. Vinegar is also put into mayonnaise for flavor which some people favor while others do not. If you wish to eat mayonnaise with no vinegar in it, you should try making it from scratch at home.