3 dates - Guy makes no move. Girls?

Belgie
A friend of mine (who isn't on this site) was talking to me last night about this guy she had gone on 3 dates with.

First of all, he asked her out. They went out on 3 dates, and he initiated all 3. But on the dates, he never touched her, never so much as held her hand or linked arms, or tried to kiss her. Not once. Not even a little bit.

Now, my friend is a very very good looking girl, blond hair, blue eyes, great smile, full rack. She's also very friendly and down to earth. (I've never seen her intimidate a guy, because she's so good at putting everyone at ease.)

But she was confused about why this guy did nothing.

He asked her out again, for a 4th date, but she said No. He replied "Ok. I thought so." or something like that. She sent him a text saying "What do you mean 'i thought so?' " but she hadn't received a reply to that. (She checked her phone rather obsessively last night, looking for that answer. I think her ego took a blow - like she's thinking .. "what's wrong with me" instead of "what's wrong with him" )

Now, she asked my opinion. And I thought about it. I could only come up with a few possible reasons.

1) Incredibly shy. - But I dismissed this, because he asked her out repeatedly, and he wasn't quiet or anything on the date.

2) Incredibly old-fashioned - I dismissed this because even an old fashioned guy would have linked arms within 3 dates, even if just to walk on the road-side of the pavement, while walking together.

3) He didn't feel attracted to her - I dismissed this as unlikely because he wanted a 4th date and she really is a good looking girl.

Eventually, the only other thing I could think of was... he's gay. And still in the closet.

When I suggested this, she said his brother was gay. I said this might mean he was under pressure from his parents to produce grand children. Maybe he felt he couldn't come out, if his brother already had.

My friend doesn't know about GAG, so I thought I'd run this past the ladies here, and get your inputs. What do you think was "wrong" with this guy? Why didn't he make the least little move after 3 dates?
3 dates - Guy makes no move. Girls?
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