Why don't we see a lunar eclipse every month during the full moon?

It is because the moon is not actually parallel with the earth. This may not be the full answer...

It is because there axis of rotation is different. They are not parallel. In that case, during the full-moon, it's not necessary, that we will see a lunar eclipse. Lunar eclipse occurs when moon comes in-between of the Sun and the Earth. 

Hope this helps!

Answerwavelength;