It appears they are trying to get s much for the seller as possible by first squeezing the lower offer. Expect them to do likewise to your buyer's offer if the number increases beyond their amount.
Essentially they are looking to create a bidding scenario.
Most likely, there was some variation in the terms.
Or if there wasn't a variation in terms, it still could be that the other buyers appeared more qualified, and thus stronger prospects. (The flip side, of course, is that your buyers may somehow have appeared somewhat less qualified, shakier somehow.)
You don't say what the house price was, and that's important to gauge whether $1,000 over the other offer was significant. If you're talking about a property listed for $25,000, then $1,000 is a measurable difference. If the property was listed at $250,000, then $1,000 isn't very meaningful.
On top of that, the listing agent may just be trying to start a bidding war. If he/she can get the first set of buyers to counter at a price higher than yours, then the agent's gotten more for the buyers. Let's say the house was priced at $100,000. You offered $101,000. The sellers counter at $105,000. If the first set of buyers comes back at more than $101,000, then they'd go with the first buyers. If the first buyers don't counter, then they'll accept your offer.
Once an offer is countered, it's dead. Yours might be the better offer, so they're willing to risk killing the slightly lower-priced offer, knowing yours is still there. In that scenario, there wouldn't be much reason for them to counter your offer, risk losing you, and then accepting the lower offer.
There's lots of strategy involved, obviously. Your broker might be able to help you some more.
Hope that helps.
That would be perplexing to me as well. However, "same terms" meaning what?
If they are exactly the same terms, meaning -- how much of a down payment, how strong is their financing, type of financing et cetera, then it could be something as simple as the sellers were offended in some way by the buyers with the higher offer. I've seen this happen more than once.