Why didn't Great Britain give the colonies voting rights?

"We the Colonists" wanted our own law. The English didn't think us very valuable unlike say India, Egypt or South Africa...let alone equal to the Caribbean and the Spanish possessions. The "United States" did have a vote on its Constitution though. That came after the War of course.

Apparently looking at the evidence the British didn't give "the Colonists" the right to vote because we wanted it.

Apparently "the Colonists" were willing to fight for that too. The Boer War was no cakewalk for Great Britain either...

In 1775, the only people allowed to vote in England were men who owned a minimum amount of real estate. The wealth of the person was irrelevant and if a wealthy merchant wanted to vote, they had to become land owners. Only about 3% of the men in the entire country qualified and the other 97% and all of the women were ignored. And those who were able to vote had absolutely no say in the selection of members of the House of Lords.

The colonists did not want the right to vote and it was rarely mentioned in any of the voluminous material issued by the supporters of independence between 1770 and 1780. They understood where they stood in the King and Government's view of taxes, finances and political power, and it was on the bottom and was going to remain there.

This is not a complete answer and partly a comment on some of the other answers, but:

It is true as some have said that the British Parliament then was not and not expected to be directly representative in a modern democratic and numerical sense of the will of the people; but nor was the United States Congress initially; until the early nineteenth century several states had property requirements to be able to vote.

What had been the Parliament of England and Wales had already been enlarged once to include representatives from Scotland by the Act of Union of 1707 and would be again by the Acts of Union of 1800 to include representatives from Ireland, so it was not inconceivable that colonial representatives might have been added too if that had seemed a workable compromise.

However, given the time it took to cross the Atlantic by sailing ship it might not have been very practical.

The delay in communication between American Members of Parliament and those they were supposed to represent would have made it harder to stay in touch. Because Members of Parliament were then unpaid, the length of absence from their farms and businesses that would have been required of those serving in a Parliament across the Atlantic might have been too much of a burden for many.

Travel time by sailing ship was possibly also one of the reasons for the failure of British policy in relation to the Colonies both before and during the War. It took weeks to get a report from America to London and receive instructions back; this was just close enough for governors and generals on the spot to be obliged to await instructions from London, but far enough away that by the time instructions arrived they were based on out of date information.

One reason was that in the late 18th century, Britain was trying to define who was "British." And this, led in turn to the question of what a "colony" was and "how much" representation one should have. There were two kinds of colonies.

The first kind was fundamentally empty land (America, Canada, later Australia), settled mostly by people of English descent. These colonies could be considered "transplanted" parts of England. Some, but by no means all, people on the British Isles would consider these people British.

The second kind of colony was territories like India, and late Africa, that were conquests, rather than settlements where "Englishmen" established their rule over non English peoples. Few people anywhere would consider the "natives" of these lands British.

Culturally, it was easier to give representation to the first group of people, who were (mostly) of English descent anyway. But the logistics of the time made this difficult; there was no air travel (only sea), and no telephones or radios to connect e.g. England and America. At best, the colonies could elect represenatives who would be seated in London. With Canada and Australia, England learned from the American example, and also benefited from the better transportation and communication of the 19th century. Perhaps in those cases, it was a matter of when, rather than whether they would gain representation.

With the second group of colonies, the question was one of "who is an Englishman and who should be represented?" England was a very class conscious society at the time, and controlling for education and economic status, there were large social gaps between being a Londoner or a resident of a northern city like Liverpool or York. Within the United Kingdom, the difference between an "Englishman" and a Scots, Welshman, or "orange" Irish was significant. After that, there were major (perceived or real) differences between people in the British Isles and those "offshore" as discussed in a previous paragraph. Finally people like "Indians" never got anything like full representation; if they had, they would have "swamped" the British empire on sheer numbers.

Attempting to answer the actual question, Giving the colonists seats in Parliament would not have suited the aims of the parliamentarians and therefore it did not happen.

In contrast to the acquisition of (most of) Canada from the French (ignoring the presence of the First Nations and their standing governance of course), the Colonies that eventually became the first thirteen states (of the USA) were all initially created as commercial ventures chartered by the crown. As such they were expected to contribute to their own upkeep and defense. This expectation eventually became contested before Parliament due to its move to tax the Colonies to recoup the costs of the "French and Indian War" (it goes by multiple names, but can be seen as an offshoot of the Seven Years War), which was in fact portion of a world-wide conflict and one to which the Colonies had already contributed much blood and treasure.

In fact, I have heard it quipped (in discussions with other people) that taxing the Colonies was a bit of a choice pastime, like fox hounding, for some parliamentarians. This exaggerates matters to an extreme, but such a statement wasn't entirely without motivation. After all, the Colonies were expected to pay tax like any other commercial venture, even if those taxes bordered on the absurd.

And, hopefully, that gets down the the core of the matter. By the time the Declaration of Independence was penned the Colonies had tried multiple times (in contrast to the assertion of Macpherson quoted above) to be taken seriously by Parliament and treated as something more than a cash machine for the treasury and the initial colonial sponsors. Many colonists were also enraged by the efforts of the crown to restrict white settlement west of the Appalachians, in adherence to the treaty that ended the prior North American / European conflict in 1763. When it was all added up, the Colonies had had enough of Parliament (IIRC, opinion on the crown was mixed) and decided that they were going to engage in the adult act of separation instead of the presumed childish one of further supplication.

Because residents of Great Britain also had "taxation without representation". Britain in the 1700s was not a democracy. Members of Parliament were not members of the general public, and were not elected by the general public. Even when elections happened, they were not in the least fair, and the voting areas had nothing to do with the numbers of voters or the total number of people there (see rotten boroughs). Higher-class Americans such as Ben Franklin might have been on a level where they could have had a vote if they lived in Britain, but they wouldn't have had a hope of being a member of Parliament.

So Britain (or more precisely King George III) wouldn't have dreamed of giving the colonists rights which native Britons did not have.

Great Britain considered the colonies represented through virtual representation and as James Macpherson wrote in 1775

Had the Americans, instead of flying to arms, submitted the same supposed grievance [as the taxed though unrepresented Palatine counties in England had], in a peaceable and dutiful manner, to the Legislature, I can perceive no reason why their request should be refused. Had they, like the County and City of Chester, represented, that "for lack of Knights and Burgesses to represent them in the High Court of Parliament, they had been oftentimes TOUCHED and GRIEVED with Acts and Statutes made within the said Court, derogatory to their most ancient jurisdictions, liberties and privileges, and prejudicial to their quietness, rest and peace;" this Country [of Britain] would, I am persuaded, have no objection to their being represented in her Parliament...

It should also be noted that the American revolution was an American civil war between secessionists and loyalists.

It must always be remembered, that they are represented by the same virtual representation as the greater part of Englishmen; and that, if by change of place, they have less share in the legislature than is proportionate to their opulence, they, by their removal, gained that opulence, and had originally, and have now, their choice of a vote at home, or riches at a distance.

Samuel Johnson, Taxation No Tyranny