Tomatoes are members of the nightshade family. (So are several other New World crops, including potatoes, peppers, eggplants, and tobacco.) Many nightshades store their pollen in a tiny, tightly wound packet in the middle of each flower. In order to release the pollen from its packet, a pollinator needs to shake the packet in a very specific way. The packet is very strong, but it is subject to mechanical resonance. If it is shaken at the right frequency, the vibrations get stronger and stronger, and eventually the packet will burst into a shower of pollen. (It’s the same principle that makes it possible for a human singer to break a wine glass.)
Basically, to get a tomato flower to release pollen, you need to touch it while playing middle C. It’s called buzz pollination. Here’s a before-and-after photograph of a tomato flower being tapped with a tuning fork:
Of course, a trait like that cannot evolve unless there are pollinators in the area that can go along with it. These nightshades all evolved in the Americas, and indeed, there are a number of New World pollinators that know how to sing for their supper. In North America, the most important of those are the bumblebees.
Honeybees are not native to North or South America. They did not evolve in an area where nightshades (or other plants with similar properties, such as blueberries or cranberries) were an important pollen source. Therefore, they were never selected for skill at buzz pollination. There’s no reason to expect them to be any good at it, and it turns out that they’re not. In fact, they’re so bad at pollinating tomatoes that if you’re growing tomatoes in a greenhouse and you can’t get bumblebees to visit your plants, plan B is to pollinate them all by hand (which is as inconvenient as it sounds.) Honeybees aren’t even part of the picture.
If you like tomatoes, then bumblebees are your friends.