For the most part they are afraid they will lost the “right” to kill their baby on demand.
Also free birth control.
I sincerely don't understand this preoccupaton / obsession of the Left with "free" birth control. (Whenever some Leftist I know talks about "free" this or "free" that, I point out that only sunshine and fresh air are truly free, that "free" in this case means that someone else [i.e., taxpayers coerced by threat of police force] are actually paying for it - but then they'll retort that they also have no choice about paying for roads and wars, etc.)
What they don't seem to realize is that birth control (i.e., "rubbers") are already nearly universally available, and very cheap - so why the insistence that they be made even cheaper?
Of course, when the Left say "'free' birth control," they also mean "'free' sex-change operations," "'free' abortions," "'free' kindergarten sex education," etc.
Regards,