Beowulf is not a hero for one main reason. His actions are driven by pride and self glorification not the desire to help other people. This becomes evident as we examine Beowulfs main three battles and the events surrounding them. The battle between Grendel and Beowulf shows Beowulfs desire for pride over the desire to help others. For instance Beowulf fought Grendel with his bare hands and fought Grendel one on one while his thanes watched.
The reasons for this were Beowulf new he would look better if he beat Grendel with his bare hands and on top of that he had his men watch instead of help so the great battle of Beowulf and Grendel could be told to everyone. These actions jeopardized his chances of winning and if he had lost the Danes would have continued to suffer the attacks of Grendel. Beowulf was not concerned with this though he was more concerned of how much glory he could squeeze out of this exploit.
The outcome of the battle was of course Beowulf winning and the people showering him with affection. This is by far the most valiant act by Beowulf but it cant be overlooked that he was obviously looking for glory and the Danes happen to benefit. The next battle is Between Beowulf and Grendels mom. Beowulfs drive this time is the revenge and more glory seeking. Beowulf is successful in killing the troll wife and before he leaves her den he takes Grendels head.
Why does he take Grendels head for a token of his great power of course. This battle didnt even need to take place considering Grendel mom had her revenge and may not have come back to the mead hall. Its doubtful it ever even crossed his mind because this gave him another chance to achieve fame but this time its not really for the greater good. Beowulfs final battle with the dragon is where his actions come to an end. This is after the dragon has stopped attacking and probably wont again.
Beowulf doesnt even need to go after the dragon but he does anyway ignoring Hrothgars warning of watching for pride and old age. So for the main reason of pride and glory Beowulf does go after the dragon but in the most insane way. Beowulf brings eleven thanes who arent even supposed to help in the battle and even suggests he would have fought the dragon with his bare hands except it breaths fire instead of having a whole army dispatch the dragon with himself leading.
Now the outcome of this battle is the dragon and Beowulf are killed. Now the effect is bad for Beowulfs people the Weders because now there great leader is dead and they are doomed. These three examples show a pattern. As time goes on Beowulfs deeds do less and less good until they actually do bad. The constant though is his lust for glory and pride which eventually is his downfall. This is why Beowulf is not a hero but a glory monger.