Why did British PM David Cameron resign following the Brexit vote?

Cameron was the leading figure of the "Remain" campaign. He had strongly supported Britain's connection to the EU and had warned against the disasters that could befall Britain (be he right or wrong, we have to wait and see) should the vote go for "Leave".

Now the British public have decided that the future of the EU does not involve them, Cameron's position becomes almost untenable after his vociferous support for the opposite view and having a Prime Minister guiding a country through the upcoming changes that he does not want may not be for the best. Cameron obviously feels this way and although stating he will stay in office for the present to "steady the ship", he will stand down in October.

He fought for the side which lost he will not resign until October.

He explained it himself. The next stage is to negotiate the "divorce settlement", and as he didn't want to leave the EU, he's not the man to do it because he wouldn't believe in what he's doing. It's far better for someone else to do it.

He was embarrassed and he fought hard for it. He lost so he resigned.

He made himself look an idiot,with his pathetic "threats"

He joined the losing side.

He was on the losing side.