In my personal experience questioning religious dogmas and asking for reasons and logic in them is not very productive endeavour.
They are as they are. They are to be upheld, not questioned and subjugated to rational thinking.
If you ask about religious reasons why dogs could be considered as haram, in article "Dogs in the Islamic Tradition and Nature" by Dr. Khaled Abou El Fadl, published in Encyclopedia of Religion and Nature, s.v., by Continuum International in 2004. it is stated:
The essential point conveyed [...] is that dogs are impure animals, or, at least, that their saliva is a contaminant that voids a Muslim’s ritual purity. Hostility to dogs, not just as a source of physical but moral impurity, are further expressed in Prophetic reports claiming that angels, as God’s agents of mercy and absolution, will not enter a home that has a dog, or that the company of dogs voids a portion of a Muslim’s good deeds. Cultural biases against dogs as a source of moral danger reach an extreme point in reports that claim that Prophet commanded Muslims not trade or deal in dogs, and even to slaughter all dogs, except for those used in herding, farming, or hunting.
So, the mayor concern about dogs in Islam is not about their physical condition, health concerns or general cleanness, but about the ritual uncleanness and the effect of that to the religious life of a Muslim who comes in contact with the dog.
If you ask about rational, scientific reasons, amongst the few allegations that can be tested are numerous ones by Muslim scholars that dog's saliva is not just ritually impure, but a real health hazard. Modern science has shown that those concerns are not just false, but it is in fact shown that dog's saliva has antibacterial properties and that there are no particular scientific and therefore rational reasons for avoiding any contact with it if the dog is healthy, as is the case with any other animal or even humans.
Source: "Antibacterial properties of saliva: Role in maternal periparturient grooming and in licking wounds" by Benjamin L. Hart & Karen L. Powell, Department of Physiological Sciences, School of Veterinary Medicine University of California, Davis, CA 95616 USA
While avoiding dogs as social animals that could potentially spread a disease from one human to another might have been a valid reason 1400 years ago, in modern times, since we have modern medicine and sanitation, very little harm can come upon pet dog owner so there are no scientific reasons whatsoever to avoid dogs.
One exception is if a person is allergic to dogs. Allergies are caused by dander, saliva or urine of dogs, or by dust, pollen or other allergens that have been carried on the fur. Allergy to dogs is present in as much as 10 percent of the population, according to American College of Allergy, Asthma & Immunology.
In general, countless dogs lived along humans throughout our history and still are living in households all over the world without any (or neglectable) problems whatsoever.
So, to conclude, if you ask for modern, rational and scientific reasons that confirm religious "reasoning" of Islam about having a dog as a pet, there are simply none!