How is that a barrier? Extremely problematic? What the heck?

First, note that it's my impression that logic and action are more dominant with men. Based on my experience on life, women, men, and relationships, logic and action seems to strenghten men's inherent identities. Men feel manly when they build stuff and solve problems, and that's generally essential to a male identifying himself as a man. This applies to cocky behaviour and winning women, too.

Now, women can certainly do both. I know women with high capabilities in logic and action such as my wife but the thing is that women often choose not to: their identities are enforced by other things in life. Unlike with men, for women it's not essential to exercise logical problems in order to be a woman. My wife doesn't rediscover her feminine identity in solving problems and fixing stuff eventhough she has done and succeeded in that before we met. My daughter is more interested in fixing bicycles and learning to use the tools in my toolbox than my son is, but it's the other things that she already does that she's using to learn how to grow up to become a woman.

Thus, I suggested the especially masculine trait of enjoying logic might contribute to the gender bias of programming as it seems to contribute to the gender bias of other activities, too. (Or it might not, but I didn't happen to suggest that.)

It's not a barrier, however. It's choosing not to drink, even if brought down to the water. And that's perfectly okay!

This might just be too much to accept for people of naivete. Men and women are different and there's generally no way around that in the long run.

EDIT: Back to the topic: programming doesn't give a squat about whether you're a man or a woman. It only requires logical capabilities and the willingness to use them. It doesn't dictate where the willingness comes from and for what I know, my fellow programmers don't give a rat's ass who wrote the code. They would accept women where they accept men because gender isn't a criteria in communicating with source code.

There is no way to make that assumption irrelevant. In absolutely no way is programming a perfect meritocracy, and social factors come into play just as much as any field. If the pervading attitude is "men are inherently better at this task," why would a woman want to enter the field?

Besides, if programming ability could be accurately quantified, there wouldn't be a constant stream of articles on how difficult it is to separate the wheat from the chaff when hiring.