They didn't force themselves in. As Huddy has said previously, you need to understand how football was back then to understand what happened properly.
Supporters were used to be treated like animals, being packed into pens so tightly that they could barely move through their own will. I remember talking to an old teacher of mine who was at Hillsborough a year or so before the disaster and he told me how he ended up about 20 meters from where he was originally standing by the end of the half just through the pressure of people around him because they were so overcrowded. My dad also told me how a friend of his lost both shoes at a game (not at Hillsborough) through people stepping on the back of his feet because they were so tightly packed in to the pen.
To those entering the pen there was nothing unusual - it was the norm to be overcrowded. And if you've been in any crowded area where a large number of people are trying to get to the same place (even waiting to get on a tube or a bus), everybody gradually squeezes forward inch by inch but it those at the front that run out of room first.