Everyone knows (we hope!) that you call the balls on your side of the net, but you also have an obligation to be fair and call your own balls out if you see them out. There is however one exception to this rule...
In a quarter final match between Roger Federer and Robin Haase in Rotterdam, a couple of years ago, Federer hit a first serve, and although there was no call from the umpire or line judges, Federer said it was out. Without waiting to be contradicted, he took a second serve. Haase was surprised and so was the commentator.
“Are you actually allowed to do that,” she asked. The answer - and sorry about this Rog - but in a Local Tennis League match, the answer would have been "no" (though it would be brave person who would question it).
There are rules in tennis and then there is The Code, otherwise known as The Players’ Guide to Fair Play and the Unwritten Rules of Tennis. It is considered binding enough to be part of the USTA's tennis officiators handbook and says players should follow it, "except to the extent to which an official assumes some of their responsibilities". Its states things like "Courtesy is expected" and that in an unumpired match players makes calls on their own side of net. But it also says if a player sees their shot is out, they should say so. The only exception to this is on your own first serve. Even if you see this is out, it is not your call to make.
The Code does not give its reasoning but it would the server an unfair advantage. If it was allowed, the oppoent could hit a winner on the return only to have the serve say the ball was out.
In the pro game though things are not on the age of Hawkeye quite so simple. Players can challenge a first serve even if it seems to be against their own interest. Andy Roddick did this in a match against Monfils at the Tokyo Open 2010 quarter finals. The umpire called Roddick's serve in and Monfils hit a winning return. So Andy challenged the call and the ball was revealed to be out. Andy got a second serve.
The Code summaries why all this matters: "The prime objective in making calls is accuracy. All players should cooperate to attain this objective."
And to be fair to Roger Federer he does. In a 2017, Hopman Cup match against Alexander Zverev the umpire called a Zverev serve out. Federer told Zverev that if he challenged the call, he would find that it was in. Zverev did so, and the Hawkeye revelaed that Federer was right. Jack Sock, showing similar sportsmanship, made the identical gesture when playing against Lleyton Hewitt in the same tournament the year before. It might lose you the point but it certainly wins you friends.