I realise that this post is a few days old, but seeing how no one has answered, I figured I would try and provide some information.
The short answer to your question is that Britain was thinking of Empire and their holdings in the region, as well as the balance of power between themselves and France in the Middle East rather than the religious, ethnic, and national interests of its inhabitants when dividing the Ottoman Empire after World War I. The details, of course, are much more complex.
Generally, when people refer to the French and British "carelessly" drawing borders in the Middle East they are referring to the Sykes-Picot Agreement, which was a secret agreement made between the French and British (with various promises made to other parties during negotiations) in 1916, which would partition the lands previously controlled by the Ottoman Empire after World War I. A map of what the agreement proposed can be seen here.^1
As you can see from the map, the borders of the region remain much as they are today. Consulting this map allows for a comparison between the modern borders and the lands of the Ottoman Empire in the lead-up to and during much of the Great War. It is also important to note the areas of British and French direct rule in the first map, which are surrounded by much larger Arab-controlled areas that operate as Protectorates of Britain and France, respectively. This map, as well as details from the Sykes-Picot Agreement itself demonstrate that France and Britain were primarily concerned with controlling key ports in the region and less with the people who reside there.^2 Together the differences from earlier Empires and governments - as well as ethnic and religious differences within the areas - coupled with the overt economic interest of the new borders have led many to criticise the Sykes-Picot Agreement as being careless.
The other major concern is that the agreement was made in secret, without the consent or input of the residents or political leaders of the region. Samir Saul, though writing in French, offers an excellent overview of the duplicity of the agreement:
France's installation in Syria was the result of a disputed, tortuous, and hazard-strewn process. In correspondence which extends from July 1915 to January 1916, Great Britain gives Sharif Hussein, the guardian of Mecca, a glimpse of the constitution of an independent Arab kingdom in exchange for an Arab revolt against the Ottoman Empire: "At that time it was not yet a question of sharing the skin of the Turk, but of killing him." The revolt began in June 1916 and the Arab contingents entered Damascus on October 1, 1918, but Great Britain did not keep up its end of the bargain. In May of 1916, Mark Sykes and François Georges-Picot had secretly divided the territories of the promised Arab kingdom between Great Britain and France. [translation mine] ^3
Recent critiques of the Sykes-Picot Agreement are usually along these lines. It is not so much that the borders drawn are arbitrary, but how they were drawn that becomes the issue: in secret, duplicitously, and in the direct service of Empire. Or, as Pinar Bilgin put it recently:
The point about Sykes–Picot is not (only) that it was a secret agreement concluded between the colonizing powers, but (also) that it was shaped by a discursive economy that allowed for the international society to decide the fate of those that were deemed as not-yet capable of governing themselves. ^4
Hope this answers your question.
