The rap on Rex Grossman is that he will never change, that he either can’t or won’t. What cost him his job as starting quarterback of the Washington Redskins wasn’t that he threw too many interceptions in a single game or season, but the suspicion that he’ll continue to throw the same balls over and over, compulsively. You can live with a guy who makes mistakes. But you can’t live with a guy who repeats them.

The issue with Grossman is not his throwing arm, but his mule head. You can hear the hint of obstinacy in his words when he discusses his benching after five games.

“The frustrating part about it is that I do think they were good performances,” he said.

If Grossman really believes that a league-high 11 turnovers is a good performance, then it means there was more of the same, and maybe a lot worse, still to come. The Redskins were right to replace him.

Why Grossman persists in playing the game this way is the great riddle of his career. To listen to him, every interception stands alone, with a set of specific unfortunate circumstances, the varied subtleties of which outsiders can’t understand.

“You want me to generalize?” he said. The implication being that he has a good excuse for some of them, and we do him an injustice to criticize. “Any time you don’t produce enough points and statistics it leaves room for judgments. So, I had an opportunity to make it clear as day and it wasn’t.”

What is clear as day is Grossman is the absolute worst quarterback in the league when it comes to interceptions, not just this season, but over almost a decade. From 2003 when he entered the NFL through 2011, Grossman has the highest interception percentage of any quarterback in the game. That’s no generalization. That’s a fact.

The Redskins gave Grossman the most golden of all opportunities, a fresh start, and he turned it into the same old story. He made the present look exactly like his past, and he showed no sign that the future would be any different. His steadfast refusal to re-examine his judgment has now lasted through tenures with three teams, and Redskins Coach Mike Shanahan, with unusual bluntness, suggested Grossman eventually will be out of work if he doesn’t experience an epiphany.

“What you have to do to play at a high level as a quarterback in the National Football League is you have to eliminate those mistakes,” Shanahan said. “And that usually comes with experience. And if you keep on making those mistakes, you lose your job and you’re either second team or third team or out of the league.”

One epiphany Grossman needs to have is that the benching was self-inflicted. The Redskins were surely reluctant to turn to the untried, doe-eyed, apple-polishing John Beck. Grossman is experienced and enormously popular in the locker room, commanding in the huddle yet affable off the field. Everyone on the team sympathized with the difficulty of making judgments on the run, and understood that mistakes are inevitable when deciding whether to gamble or protect the ball.

Everyone, from Shanahan to Santana Moss to Brian Orakpo, wanted to see him succeed.

The Redskins weren’t wrong to take a chance that Grossman could change; players remake themselves all the time. There are quarterbacks across the league who capitalized on a change of scenery, used fresh starts to redeem their reputations and changed the arcs of their careers.

What plagues Grossman is an attitude, not some physical limitation or written-in-stone destiny. He’s simply careless with the ball, and that ought to be correctable.

The issue is “maybe a mind-set,” he admits. Take his first interception against Philadelphia, on the opening drive when he looked to Fred Davis but was picked off by Kurt Coleman. The Eagles wound up with the ball on their 3-yard line. You could look at that as a fairly harmless change in field position, which is how Grossman is tempted to think.

“Better than a punt,” Grossman said before acknowledging, “but it didn’t feel like a punt.” It felt like a 14-point swing. The Redskins lost all their energy, the Eagles took the ball the length of the field to go up 7-0, and the first-half slaughter was on.

When Grossman talks, you can hear that he is trying to convince himself to take a different approach but hasn’t quite gotten there yet.

“Maybe the only thing I could do that would encompass all the turnovers, is just have a little more conservative approach to the fact that, one, turnovers are bad, and they’re emotional mistakes that create emotion in the stands, emotion everywhere,” he said. “So they have an odd way of feeling worse for your momentum.”

All NFL quarterbacks struggle with the tricky equations of daring and dumbness, discipline and over-caution. But that’s the sum of the job; Grossman is paid to attain a certain amount of clarity and recognition. If he would ever learn to make just one less horrible play per game — that’s all — he would be a perfectly secure starter. He’s so close to being terrific, which must make it tempting to stay with him.

But the Redskins can’t continue this way; his turnovers waste everyone else’s efforts. They have to give Beck a try. It’s entirely possible Beck won’t work out, and the Redskins will turn to Grossman again. If so, they have to hope that career desperation gives Grossman the recognition he lacks. He can change, or watch his career die.

You can’t fault Grossman for trying hard to make big plays. But trying hard is not the same as doing your best. Great performers recognize mistakes, find out why they’re making them, and fix them. They are relentless self-critics.

Maybe Grossman’s pain and discouragement over the benching will lead to a burst of illumination. We’ll know he’s gotten there when he drops the rationalizing tone, quits talking about how many good things he did, and fully owns up to what he does wrong.