So to sum up the thread so far, the OP watched a dog walker let her dog off the lead on a public footpath when she saw some local pet cats there and encouraged her dog to chase them. Her excuse was that she couldn't control her dog even with a lead on, so presumably had even less control once the dog was off the lead.
So she intentionally encouraged her dog, which she couldn't control, to chase after cats and try to catch them.
And what are some of the responses?
"Oh well the cats will probably get away OK" - you can't guarantee that, and doesn't cancel out the fact the woman is trying to get her dog to harm the cats.
"Bah disgusting feral cats" - ignoring that these are owned cats, if they were feral then they would be wild animals. Setting a dog on a wild animal is illegal in the UK except in very particular circumstances (hint - this doesn't include hunting cats on a public footpath).
"Those cats deserve it, because cats shit in my garden". I would take a guess that the majority of "cat" shit people say is in their garden is actually fox shit. Cats usually bury their waste, foxes tend to do it where they are whatever surface they are on.
"She has a right to exercise her dogs" - not if her version of exercising the dog is encouraging it to chase other people's beloved pets. Interesting that she only let her dog off the lead when they came across the cats?