Why do dogs chase cats?

And why am I made to feel like a bad owner when I let mine chase them?

Well, no more. For a start, cats are bastards. Y'ever seen how they torture rodents? Letting them run a bit away, like they have even some chance of escape before leaping on them and continuing the torture.
Eventually they get bored and just remove the head.
Moreover, cats will go where they're fed - no matter who 'owns' them. They sit in comfort on laps or cushions by the fire in the house while their canine cousins are banished outside in whatever weather meets them.

There's a cat in my street that sits and watches with this look of superior contempt as I walk my dogs past. Man, I swear, one of these days I'm goin to let 'the big fella' of his lead. That'll take the smug look of its face when it sees the dog comin at it.

See, we have nothing to learn from cats - at least nothing good. Selfishness and exploitation, the ability to slyly feign interest to achieve an end (usually gettin stroked or petted or fed).
From dogs, on the other hand, we can learn honesty, trust, bravery, loyalty and an unconditional love. Man's best friend is apt. We get companionship from them; they lead us, work for us and provide us with a sense of happiness. The great explorers of the ice world used the humble dog to pull sleds. Police forces use them to enforce law and otherwise protect the public.

Cats? Well, like I say - selfish bastards and if my most trusted of friends want to succumb to the pull of nature then tough shit on the cat. If you don't like it, keep your scrawny moggie inside. Any cat out after 5pm is fair game in my book.