Assuming they're tax breaks on property taxes (since other than sales taxes, those are the most viable avenues for a city to tax), they would lose tax revenue o

Assuming they're tax breaks on property taxes (since other than sales taxes, those are the most viable avenues for a city to tax), they would lose tax revenue on whatever property the factory is on (it is not the case that they wouldn't have been able to collect taxes on the business anyway, because the land they use is land they would have taxed had it been owned by someone else). So they may have to tax other businesses more to make up for it, which could drive those businesses away, or make them less competitive. Other businesses in the area can also be hurt by the presence of an employer who can offer higher compensation than they otherwise would be able to. And while hurting existing local businesses to bring in another could be worth it in the short run, in the long run pandering to a single company at the detriment of others could make you entirely dependent on that company and its fortunes.