Which process do plants try to avoid self pollination

insect-pollinated flowers have to attract insects to visit the flowers to carry the pollen on somewhere else

Plants avoid self-pollination by a whole range of different mechanisms. One of them is kiwifruit, and what kiwifruit does is it has its male and female flowers on different plants. So a female plant can't actually pollinate itself at all - it's got to get pollen from somewhere else.