My neighbor says I need to clean out my vegetable garden or the insects will be worse this year. Is this correct? I'd rather wait until I plant.

Your neighbor is correct. Countless insects spend winter in old plants, garden weeds and soil. They will pounce on the first vegetables you set out. Some spend the winter as adults, others in immature forms such as grubs or pupa. Still others were left behind as eggs clinging to plant stems, and they'll hatch in spring. Trash your old plants and dig up weeds to get rid of hiding places. Turn the soil if the ground is not frozen or too wet; this exposes insects in the ground to freezing weather. Throw away old mulch. Even though spring is nearly here, anything you can do now to carry away the insects and expose those left to the last few freezes will help.