LOS ANGELES (CBS) — Time Magazine’s new cover features a picture of  Jamie Lynn Grumet, a 26-year-old Southland mom, breastfeeding her child.

That wouldn’t normally be newsworthy … but in this case the child is nearly 4-years-old.

The photo — highlighting a new phenomenon called “Attachment Moms –  has some cheering, and some cringing.

Amanda Burden, reporting for CBS2 and KCAL9, went in search Thursday night for reaction from both sides of the issue.

Said one, “I think he’s a little too old to be breastfeeding.”

Said another, “I think it’s maternal. To each their own.”

Grumet told the magazine she was breastfed by her mother until she was six and sees nothing wrong with attachment parenting. The term refers to mom’s breastfeeding as long as possible, sleeping in the same beds as toddlers and spending 24-7 with their brood.

Grumet told Time that people who see her breastfeeding in public all the time threaten to call social services. “Of that it’s child molestation. I really don’t think I can reason with those people.”

Time profiles Attachment Parent guru, Dr. Bill Spears. He wrote his controversial book more than 20 years ago, one that advocated breastfeeding beyond two years. He called it beneficial, Grumet calls is normal.

Burden spoke to pediatrician Dr. Tanya Altman who says it is anything but. “When I first saw this cover, I had to do a double take. It’s not the typical scenario I see in my office or in the park. Or of a mom looking lovingly at her baby breastfeeding.”

Dr. Altman also says after a child turns 1, they no longer derive any nutritional value from breastfeeding.

Plus, attachment — she believes — isn’t teaching the child about independence. “At some point you want to teach your child independence. And you can’t team them that. They let you know when they’re hungry, when they’re thirsty but make choices on their own that they can spend time away from you.”