No! Some agents are strictly listing agents, some are strictly buyer's agents and some do both. That's the whole point of having different agency relationships. Many many years ago there were only listing agents. If you wanted to buy a house, you contacted the listing agent of each house you wanted to see. (this was called "Dual Agency"). Listing agent basically worked with seller and buyer but really didn't have any loyalty to the buyer. This was extremely unethical since the listing agent was working for the seller, not the buyer. Now we have buyer's agents who represent the buyer and take them to view listings of other agents. If the house fits the buyer's criteria, why would I NOT show it to them? It would be UNETHICAL for me not to!
If you're selling and you're concerned about listing with an agent who only lists homes, you shouldn't worry. Your home is being seen my thousands of other agents and their buyers. If you're not getting showings, then there's some other factor involved. Showing condition? Photos? Price?