Totally not a homework question, I swear. After hearing his public works being honored and blamed for decades now in all manner of books, articles, and documentaries, I think it's an important answer to get about some very proximate history that also has implications on the historic change of urban neighborhoods and how we deal with city planning.
One of the older recriminations is that the visual blight of the expressways lowered property value encouraging middle-class whites in New York City to leave for Long Island or other parts of the Tri-State suburban area. Home resale value and the real estate market does not seem to have been as prominent an issue for homeowners in the 1950's, especially for many who were first-time homeowners in the midst of mortgage repayments. On the other hand, blaming white flight on increasing inner city crime is an explanation I somewhat doubt as the "crime epidemic" didn't really hit record numbers until the mid 1970's and early 1980's well after white flight was documented.
Do we have any primary sources which attest to Robert Moses' two expressways being the direct cause for people wanting to move out of New York City?
Moses wasn't doing anything that wasn't going on in every other US city, nor were the results very different. Almost all US cities (with noticeable black populations) experienced white flight, even those that built very few superhighways. A much stronger indicator was close-knit white ethnic neighborhoods that felt integration threatened their relatively recent investments in houses as assets, and another strong indicator was forced busing and resistance to school desegregation.
Visual blight is a pretty localized phenomenon to blame for large demographic shifts.
Building infrastructure that made transportation by automobile easier and the standard mode of transportation certainly had a lot to do with the development of the suburbs and subsequent white flight. While I cannot speak of the Bronx in general, the building of freeways to downtown Los Angeles caused substantial urban flight to the suburbs which were red-lined (essentially zoned) as white only neighborhoods. So the highways provided access to the city from white only neighborhoods, essentially allowing them to leave behind aging cities for new homes in newly developed communities. So the infrastructure facilitated white flight, rather than caused it.
Edit: Furthermore, the constuction of freeway's destroyed the cohesiveness of many neighborhoods in Los Angeles. Freeway construction in Boyle Heights east of Downtown forced a lot residents to sell their properties and convinced many others to leave for the new suburbs, leaving the area of Los Angeles poor and blighted to this day. Construction of freeways through wealthier neighborhoods/cities in Beverly Hills and Pasadena were impeded and permanently canceled causing a disproportionate amount of construction to take place in poorer neighborhoods.