The problem with this thread and many similar threads is they start out with a faulty premise. Based on a couple of dates and what a couple of men said to her she is concluding that men are intimidated by her education and success. As has been pointed out this is not the case with most men. So in order to give the OP really good advice you first have to correct the premise.

I've noticed that when this happens and people tell the OP their original assumptions may not be correct then there are a few that start crying that we're not honoring the OP's request for advice or we're getting off topic, etc. etc. etc. The worst thing you can do for someone is to allow them to continue to believe something that isn't true. The OP may have met a few men like this, but she can rest assured that her education and success is not going to be what keeps her from a successful relationship. If she is not having success then she may need to make some adjustments. The first thing I'd suggest is dating people with the same relative education level and success level.

As others suggested it could be that she might give off a vibe that a relationship is not going to be a high priority in her life and her success is always going to come first. Without knowing more we can't conclude that, but it is something to look at. I've seen it mostly happen with women who meet successful men, but many of these women find out that he is always working late and even working weekends because he's driven to be more and more successful. This does spell trouble for a future relationship, and it is something to consider up front.

P.S. Telling a person what they want to hear and re-enforcing stereotypes isn't necessarily the best way to give advice.