(I need to state that I stand to neither side~)
Girls tend to seek help from the boys, especially in some way that the girl feel that a boy need to 'protect' them. For example, accompanying to go to market. It is normal, since Allah had made men to be a level higher than the woman:
"Men have a status above women" (Al-Baqarah, 2:228)
This is a fact, and it is always our (men) responsibilities to protect the women. Of course, we guys always need the care of a girl~but that can wait until the marriage. Women are the one who make the men strong~
Back to the main point, it is a nature that a girl need help from a guy. Especially in my community, since we are in a foreign land, not everybody can live on their own. Usually there is no romance involved, but guys sometimes get over their head and think that the girl admired us. It's normal though, guys love it when someone depend on them.
When the guys see the chances to make a move, then they will do everything in their power to get the girl. Maybe the girl don't see it, but guys will show that they are worth to depend on. So the girl, who doesn't has the feeling towards guys, but the guy thought that she admired him, can see the sincerity of the guy and continue to depend on him.
Girls are the type that always give something in return to someone who helped them. Somehow they feel guilty if they are not repaying. That is why girls always stick to the guy that had help them, so that they somehow can repay it. The guy will see more chances to approach the girl, and he will keep doing it. The girl, unintentionally, developed the special feeling towards the guy, even though it was never her intention from the start. After they spent their time together for some times, their feelings will grow, and at a point they will confess to each other (one of the possible ending :p).
This is one of the many cases how people be in relationship. But, the flow and the conclusion is not always the same. Maybe there are certain couple (just a guy and a girl, not yet in relationship) that gone through the same process, but has different outcome. Most of this post are my opinion because I had seen through this event a couple of time~
Maybe you all have different opinions, but this is only from my point of view~So don't get mad too quick! I know there will be specific person who will argue with me on this. haha