While you may be using a real estate professional in your home shopping and purchase, you're the ultimate decision-maker when it comes to the deal, and the price you're going to pay for the home. You shouldn't be shy about communicating your desires to your real estate agent.
By all means, listen to your agent's market statistics and advice. If you've gathered all of that information, and you want to make an offer lower than advised by your agent, discuss it with them. The decision should be influenced by your ability to walk away from the home and buy another. If you have been shopping for a long time, and this is the only home that meets all of your needs, would it be a terrible thing to have to walk away because of a low offer flatly refused without a counter offer?
If you have a couple more homes that meet your needs as well as this one, and you can walk away without feeling like you missed the deal of a lifetime, then make a lower offer if that’s what you want to do. There is no way to know the ultimate motivations of the seller, and you could be pleasantly surprised.
Just remember that there is still an inspection and repair negotiations to come. If you're congratulating yourself on the drubbing you gave the seller in the home price negotiation, you may find that there is no flexibility in the repair negotiations, with the seller taking a hard line.