Henrik Ibsen's Hedda Gabler tells the story of a woman whose character traits alone can create a story of their very own. Hedda embodies every negative characteristic that a woman could possess. She is ill-mannered, cold-hearted, easily-annoyed, and ungrateful. She is also jealous, cunning, and dishonest. This reveals the real nature of a woman so empty inside, and so shallow at the same time, that her own inner misery is consistently in search of company.
All these descriptors easily lead us to conclude that Hedda may or may have not had a real good reason to burn Lovborg's manuscript: She may have simply done it as yet another manifestation of how worthless and cruel her behavior can be.
We do know, from the story, that Hedda confesses to her husband how the reason why she burned the manuscript was supposedly to help him in his competition against Loveborg for an academic position. According to her, if Lovborg's manuscript is out of the way, then the competition will be more favorable for her husband.
Yet, having described Hedda, we find that it is hard to believe that she would sacrifice anything for anyone. She is first, second, and third in her view. Therefore, the best assumption is that Hedda burned Lovborg's manuscript because her own state of miserable and eternal frustration always leads her to wish the worst on anyone who would desire a better life. After all,
a) She is jealous that Lovborg befriended Thea
b) She is indeed jealous of Lovborg's talent over her boring husband's
c) She demonstrates a psychologically unfit apathy for bonding with people.
d) She is just plain mean.
All this being said, Hedda shows us that her destructive tendencies leave desolation, sadness, and even death, across her path. Hedda is not a woman to meddle with. She is indeed capable of anything.