AFAIK, Apple doesn't lose customers, it just doesn't gain as many as the overall market - and it still outpeforms the other mobile makers on revenues/profit by a huge margin.
1) he shows no graph depicting anything to do with market share, let alone one showing it sliding. There's two graphs, one showing a dip in sales volume, another showing a dip in overall smartphone buying.
2) he did explain why he thought that, near the end of the article
http://www.macrumors.com/2016/06/02/meeker-2016-internet-tre...
So market share is declining.
The reasons he gives for Apple's market share to increase are not new. They have been losing ground despite the conditions he describes. If we wants to argue that Apple is going to reverse this trend he needs to give new reasons.
Apple's market share continues to slide, as his own graph shows. If he expects Apple's market share to grow he should explain why. So far all the indicators point the other way.