If so, you're not alone. The cover shows a 3-year-old standing on a chair to reach his mother's breast, and it's already been called "inflammatory" and "sexualized" since the magazine tweeted it this morning. The photo illustrates the magazine's article on attachment parenting.
As a related story on extended breast-feeding in the issue explains, the squeamish reaction is uniquely American. The World Health Organization recommends breast-feeding until at least age 2, and the average age of weaning worldwide is about 4; a natural age of weaning humans is between 2 and 7, according to the American Academy of Family Physicians.
In the United States, although the American Academy of Pediatrics recommends exclusively breast-feeding for six months, only 15 percent of women do (44 percent breast-feed their children some at 6 months). By the time their children turn 1 year old, fewer than 25 percent of American mothers are still breast-feeding.
Those numbers help explain our surprise, but maybe not the extent of the photo's emotional impact.
Some theorize that it's the sexualization of breasts in the United States that leads to discomfort. Forbes wonders if it will be bad for Time's business, while Slate posted a blog that refers to breast-feeders as a "cult" and the movement as "oppressive":
"There is the very basic objection that it is virtually impossible to do what the advocates say is best for your baby and have a job, which the vast majority of American mothers have these days," writes Hanna Rosin.
The Time story isn't the only recent breast-feeding episode to grab headlines: In March, Harpers ran a story called "The Tyranny of Breast-feeding," pointing out that bottle-feeding seems to be under attack. On the opposite side, mothers have staged nurse-ins at Target and Facebook in recent months.
The woman in the picture is 26-year-old Jamie Lynne Grumet of Los Angeles, who weaned herself from breast-feeding at age 6.
"The more people see it, the more it'll become normal in our culture," she says in the magazine. "That's what I'm hoping. I want people to see it."
Time had an idea of what kind of reaction the photo would provoke.
"From the moment that we started talking about this story as a cover possibility, it was like I couldn't get out of the meetings," Forbes quotes Time managing editor Rick Stengel as saying. "There was so much opinion and passion about it and discussion. What that told me is, boy, this is a story that people care a lot about."