It is not very often we get a house listed for sale beside another one, side by side. However the dynamic of a REALTOR® working with a buyer client that inquired on the listing is showing a a similar home, perhaps next door, similar style and similar price.
"How can he/she do that isn't that a conflict of interest or something?"
The answer is Yes they can, and more importantly yes they should. As a seller perhaps you are thinking "well shouldn't you just show my house and only bring the buyer to my house not a competing listing?". That typically lies with the nature of the relationship or contractual relationship you signed with your listing agent. Most typically you signed an "Agency" relationships acknowledgement that describes the process and what could happen with "dual" representation etc... I would speculate that you signed off with an option that states something like "I don't care where the buyer comes from, who represents the buyer, as long as you sell my house". So yes I may bring the buyer through your home as you've requested because yes I want to sell your house.
"Then why are you showing him the neighbors house?"
The short of it is, it is my job to show my client properties that meet what they are looking for. I would be wromng in only showing some one my listing and only my listing. That would not be fair, honest and I certainly would not be working fully in their interest now would I?
The reality is no house is the same. The floor plan may be the same or as close to as possible, but the yard is different, the sun through the windows is different, the flooring, the colours, the size of the lot etc... So by showing the house next door or down the block I am actually aiding in the process of elimination for the buyer. They essentially go through a process where they eliminate the houses they do not like.
In summary, no it is not a conflict of interest to show the buyer other properties. Putting your buyer hat on and reflect on when you bought or selected a builder you wanted options and to see a variety until you found that "one".