Before asking why insects would grow bigger, a better question to ask would be why would anything grow bigger or smaller. A great answer for this can be found here.
Now from that link one will find that insects benefit from being small because it's just so beneficial for them - literally every answer on that list applies (except for hibernation and athleticism, I guess).
So then we can look at the food-web and ask ourselves what the role of insects are. So, insects like ants and such eat other insects, plants, fight other ants, and eat dead things (so they're scavengers and part of the decomposition process). If we zoom in on ants alone, ants are in many ways the #1 predators on the planet. They're not hunting down elephants, but as a species (or group of species) they kill more organisms than almost any other species in terms of variety and raw number (except maybe humans). As prey, insects are eaten by creatures larger than themselves, like birds, lizards, snakes, anteaters (who only seem to be interested in ants), and others.
So why would ants or any insects grow bigger? This could be due to a combination of a few of different reasons:
Lack/Removal of predators: One reason why insects could grow bigger is because nothing wants to kill them. Now, increasing in size is typically considered a good thing because you can ward of bigger prey, but being too small to see/aim at is also pretty beneficial. That's what most insects are now, but if nothing was eating insects, it is plausible that over millions of years insects would grow pretty big (check out ancient dragonflies). That isn't to say ALL insects would - most likely there would be a number of smaller insects that would be preyed upon by bigger insects. This already happens now, but now in your world the biggest insects are bigger than ever.
Reduced reproductive rates: I don't know what could cause this, but it's easier to have a million babies when all your babies are small. Insects typically have many eggs, and although not all eggs survive and hatch, enough do. If this reproductive rate of some insect species decreased suddenly and significantly enough, this could quickly make this species extinct as they'd be 'outbirthed' by rival species. Assuming that this decrease in births takes place gradually, a good way to get around the problems that come with this would be for said species to get bigger. This would hopefully also increase the successful birth of a given baby insect. If you have a million babies and only 10% survive, that's still 100k babies, so your species will probably be ok. If you have only 5 babies 10% survive, that's a concern. What could cause fewer births? If some insect species was the Bruce Lee of insect species and had a formidably high kill-rate per individual, there would probably be no reason for that species to outbirth other species. This could be a reason for why insects get bigger as well.
Abundance of food: Average human sizes in every country has gone up as food became more accessible. How does this relate to insects? Many insects are herbivorous. If for some reason we had a sudden increase in vegetation, allowing there to be more than enough food for insects, it is plausible that some species would grow in size. This could also mean that the predators of these insects could also grow bigger to effectively take on these large, ripped, vegetarians, or grow smaller to be able to effectively swarm larger prey.
I think that you'll have to combine multiple reasons to cause long-term size growth evolutionarily speaking. You can throw in a catastrophe here and there too. For research purposes, look up the Carboniferous period (swampy part of our history - all our coal comes from here) and the early Devonian period (this is when insects first came about). Let's not forget that both these periods had very different atmospheres - only 21% of our air is oxygen, as opposed to 30-35% back then. Also, depending on how much you hate them, consider eliminating birds. They were also a big reason why insects got smaller.
I hope this helps!