The Gemara states that mice are pursued by everyone as a retribution for their bad inclination of gnawing at everything, not only food items.
But the fact is that they must gnaw constantly because some of their teeth grow constantly and they would die if they wouldn't reduce the length of their teeth through gnawing constantly.
How then could their behavior be attributed to bad inclinations when it is due to the way that their teeth grow and which is not under their control?
Unless we could find something constructive that they could do through their gnawing.
Furthermore, it's somewhat surprising that none of the usual commentators brings up altogether this fact about their constantly growing teeth.
Mordechai Schwimmer
(a) I can suggest an explanation based on Tosfos in Bava Metzia (40a, DH v'Ki) in the name of the Talmud Yerushalmi which states: "Mice are bad, because when they see produce, it is not enough that they eat it, but they also call to their friends to come and eat together with them."
It seems that mice are considered bad only because they involve their brethren in their antisocial behavior. The latter action is not necessary merely to solve their own problem with their constantly growing incisor teeth.
(You may ask a more general question, however, and that is how can mice be considered bad when they are animals with no conscience and no ability of free choice? That is a different question which I will deal with below.)
(b) I would like to offer a different answer to this question, and I think I have support for my idea in the words of the Netziv zt'l of Volozhin, in his Sefer Meromei Sadeh here.
1. If one thinks about this Gemara, it really is not so simple. Animals do not possess "Bechirah Chofshis," free choice; they are not in control of whether they do good or bad things, but rather they follow their natural instinct. So how is it possible to say that mice receive a punishment for gnawing at everything? This is instinctual behavior which the mouse has no control over!
2. Therefore, it seems that one must say that the Gemara is merely teaching us a "Musar Haskel" from what we see in the world of nature, and from this we can learn what people will suffer if they descend to behave in a way similar to beasts.
3. It is a fact of nature that mice always eat everything. It is also a fact that they are always being chased after. People have to chase the mice in order to make sure that they do not do damage. As you pointed out, there is a natural reason why they always eat things -- because some of their teeth grow constantly. This is part of the rules of nature that Hash-m put into the world, and we can learn a Musar for ourselves from this.
4. The Gemara is teaching us not to emulate the mice, and warns us about what will be the retribution for humans who follow the bad ways of mice (and humans do have the ability to choose how to act). The Gemara teaches us not to steal from others in the way that mice do. In addition, we are informed that if someone is a thief, he will be chased all of his life. He will always be trying to run away from the police, or from the victims from whom he stole, or from being seen by witnesses.
5. I see this in the words of the Netziv who writes that we can learn from our Gemara about mice that if a person is bad to others even though he gains no benefit, people will retaliate against him just to be malicious. The Netziv writes that this is what the nature of mice teaches us.
6. The Netziv hints at the Gemara in Eruvin 100b which cites Iyov (35:11), "He teaches us from the animals of the land." The Gemara states that even if we would not have been given the Torah, we still would have learned the good traits of modesty from the behavior of cats, and we would have learned not to steal from the way that ants are so careful not to steal the food of their friends. We now may add that we learn from our Gemara in Horayos what happens to someone who always steals from others. In the end, he will be pursued by everyone.
7. So it is true that mice must gnaw constantly because their teeth grow constantly. However, mice do not possess free choice and it is not possible to say that there is reward and punishment for mice -- but Hash-m made the world like this in order to teach us what will happen to humans who do possess Bechirah Chofshis but still decide to transgress the Torah.
B'Hatzlachah Rabah,
Dovid Bloom
B"H
And why does the Gemara choose to teach this in terms of mice, instead of talking plainly about people? Wouldn't the mussar be more straightforward and effective without mentioning mice at all?
Tizku lamitzvot.
Nahum
Buenos Aires
The Gemara often uses vivid examples to illustrate it's Musar points.
In fact Shlomo Hamelech, in Mishlei 6:6, also used a similar technique when he advised us to learn from ants the virtues of being industrious and orderly.
The fate of mice is something that everyone can see, and we now try and discourage people from becoming thieves and say how they might become like mice who everybody catches in their mouse traps.
Shabbat Shalom
Dovid Bloom