Game Over, Humans Lose
Our countermeasures against insects works because they aren't coordinated. Much of what we do to prevent exposure of our bodies, food and assets works against specific pests. Screens over doors and windows work against mosquitos and other biting insects. Pesticides prevent crop destruction.
But, all of the things that we defend against can be undermined by a determined effort by a combination of species. (I'm going to focus my efforts on North American ecologies because those are the ones I know best.)
The easiest will be if the bees just stop pollinating crops. Without pollination, the world's food supply collapses in a matter of years. Perhaps sooner, if other insects and contaminate and destroy existing food supplies.
A great deal of the protection that we enjoy against insects comes from our buildings, specifically about 128 million wood-frame homes. Wood frame structures are ripe for attack by termites. Termites driven by a coordinating intelligence could avoid the bait and traps that we already place and focus their attacks on the structural wood. Attacks like this will require several months to execute so it may take a while before we humans see any results.
There are bees, wasps, and hornets everywhere. Generally they keep to themselves but if directed they could make an impressive area denial weapon. Attacking and stinging people as they leave their homes before they can reach their cars. Children will be kept indoors and people will leave only when absolutely necessary. Food shortages will start for people who go food shopping every day or every other day.
Mosquitoes are also an effective area denial weapon. Any flying insect, if there are enough of them can plug up the air intakes for automobiles or tractor trailers. Cleaning those filters is annoying and slows down the movement of goods.
Ants are capable of getting into very tightly enclosed places and chewing on things that shouldn't be chewed on. They are also capable of moving large quantities of earth, so it's possible that they could actually undermine the foundations of buildings. Attacks like this would still take time but perhaps not as much as expected.
Direct Attacks on Humans
Many insects have a painful or poisonous bite. With a swarm of attacks on a human, particularly the elderly or very young, biting insects can cause extreme illness or death. Ants can strip human bodies down to the bone.
Insects may not be able to kill every person but they could destroy infrastructure and crops that would prevent humans from eating.