Well of course we can. I got through childhood without one and our ancestors got through their entire lives.
I read an article a month or two back which was saying that microwaves zap a lot of the goodness out of food. I forget the details but the broad assertion is all one needs to know. Ever since then I've used the microwave sparingly- mainly as a way of reheating my mother's cups of tea and coffee when she's let them get cold (not much goodness in them to begin with) and never as a mode of primary cooking.
And now we've got rid of it altogether (banished it to the garage- halfway to the tip)- and its old position (space is limited in our badly designed kitchen) is occupied by a food processor.