As Muslims we consider dogs and their saliva to be impure and filthy.
Prophet (sallallaho alaihe wassallam) said:
“Whoever keeps a dog, his reward for good deeds will decrease by one qeeraat every day, except dogs used for farming or herding livestock.”(Bukhari)
"Angels (of Mercy) do not enter a house wherein there is a dog or a picture of a living creature (a human being or an animal)." (Bukhari)
“If a dog drinks from the vessel of any one of you, let him wash it seven times” (Muslim)
That does not mean that just because we are not allowed to keep dogs as pets or because they are filthy we are to be cruel to them because the Prophet (sallallaho alaihe wassallam) said:
“A prostitute was forgiven by Allah, because, passing by a panting dog near a well and seeing that the dog was about to die of thirst, she took off her shoe, and tying it with her head-cover she drew out some water for it. So, Allah forgave her because of that." (Bukhari)
“A man saw a dog biting the dust because of thirst, so he took his shoe and started to scoop water up with it until the dogs thirst was quenched, Allah appreciated his good deed and granted him entry to Paradise for it” (Bukhari)
Allah's Apostle (sallallaho alaihe wassallam) said, "A woman was tortured and was put in Hell because of a cat which she had kept locked till it died of hunger." Allah's Apostle (sallallaho alaihe wassallam) further said, "(Allah knows better) Allah said (to the woman), 'You neither fed it nor watered when you locked it up, nor did you set it free to eat the insects of the earth.' " (Bukhari)
Dog’s that are pure black in colour however should be “put to sleep” or ”put down”. The Messenger of Allah (sallallaho alaihe wassallam) said:
"Five kinds of animals are mischief-doers and can be killed even in the Sanctuary: They are the rat, the scorpion, the kite, the crow and the rabid dog." (Bukhari)
"Were dogs not a species of creature I should command that they all be killed; but kill every pure black one." (Muslim)
PS. The intellect of man is limited and as such, he will not always be able to comprehend the wisdom of divine law. Sometimes, man is unable to understand the logics of Shari’ah law.
He is obliged to accept it whether it appeals to his intellect or not.