Batsman Peter Handscomb was also left out of the tour, Australia's first since the ball-tampering scandal in Cape Town, but it was Maxwell's omission that raised the biggest stir, particularly because he wasn't on the just-completed Australia A tour to India, which meant he did not have a chance to win a spot in the Test squad. Moreover, Maxwell had said he received positive reinforcement from the selectors following his omission from the A squad, leading most to believe he was set to tour the UAE.
"If I was Maxi I'd be thinking, 'why didn't you give me the chance to actually go there (to India) and push my case to get myself into the team?'" Ponting told cricket.com.au. "That's all a bit bizarre to me. If I was Maxi and I hadn't been given the chance to play for Australia A, I'd be ropeable.
"They didn't pick him on that Australia A tour and they've said they've seen him play enough in those conditions and knew what he could do. But if you think about it now, that must have actually meant they weren't going to pick him at all. He didn't even come into calculations for that Test tour.
Maxwell, who made his Test debut in 2013, has never been able to nail down a spot in the longest format, having played only seven Tests over the past five years. His last Test was in September last year in Chittagong, where Australia completed a series-levelling win.
Ponting was most critical of the fact that Maxwell wasn't given the chance to prove himself on the A tour. "With Marnus and Travis Head going on that A tour, they gave them the opportunity to play in those conditions, they've done well and then they picked them [for the Test squad]. I'm not sure what the message is, but it's a bit confusing to me."
Ponting said the selectors needed to convey to Maxwell what he needed to do to work his way back to Australia's Test squad.
"He's someone who's desperate to play Test cricket for Australia, he wants to play any game of cricket he can for his country," Ponting said. "He's always going to be that type of match-winning player. If he comes off every two or three or four games - that's the kind of player he's always going to be. He's got enough time and skill to be able to play more Test cricket for Australia."
Fast bowler Peter Siddle, who was recalled to the Test squad because of injuries to Pat Cummins and Josh Hazlewood, also said he was surprised by Maxwell's omission. "Coming home and being around him yesterday, he was a little bit confident that he was going to be a part of this squad so he'll be very disappointed. I do feel for him, you always want your team-mates to be in and around the squad and be a part of it with you. I know he'll be shattered.
"But I know one thing he'll do is work hard and get ready to push his case for the summer. It's hard, it's a whole new-look side and a lot of changes. And obviously the direction that they're going at the moment, with three spinners in there, it does make it hard to be a batting spinner in the side. So you can see where they're coming from. He's got plenty of opportunity now to get ready for the summer to push his case."