Commuting by bicycle does not make you incapable of dressing like a real person. I know this, because I commute by bicycle, and I almost always dress like a real person.
Bicycling generally does demand wearing trousers, if one is going at any speed at all, and doesn't own a cruiser. Getting on and off a non-ladies' road bicycle in a skirt can be complicated and involve dislocating one's hip in the interests of modesty, which is not really to be desired. But trousers come in an impressive range of fabrics, and they don't all make you look like a bicycle courier.
Unless you actually are twenty-three, and a bicycle courier, and the weather is always bad, it is not necessary to dress exclusively in nylon clamdiggers. You look ridiculous.