This is the lie he tells himself: Obi-wan wouldn't understand.
The truth is more complex.
He knows that they are more than Kenobi and Skywalker, Obi-wan and Anakin, TheTeam (capital letters and all). He knows that they are much more than (ex) padawan and (former) master. And he knows, deep in his heart of hearts, where not even Sideous in the guise of Palpatine has been able to pry, that upon confessing his overpowering and highly inappropriate attachment (and subsequent marriage) to Senator Padme Amidala, Obi-wan will first take a deep breath, then proceed to choke almost comically on thin air when the delayed reaction of shock and incredulity hits him. But by the time he exhales, most likely only made possible with several hard thumps on the back courtesy of Anakin, all will be forgiven.
He probably wouldn't even tell the council if Anakin asked him not to.
Sometimes it seems like Obi-wan has spent the entirety of his adult life running interference for him against the far too judgmental and persistently suspicious body of Masters. And he knows that despite the respect (and deference and outright awe) that others increasingly afford him, his Master suffered dearly for his unwavering support of Anakin, especially during the early years of his apprenticeship.
It is because of this that he decides to solve his problem on his own.
He is a knight now. He was the one who gave into his attachments; who rushed into marriage on the eve of a galactic war. He does not need to burden Obi-wan with his mistakes. He will find a way to make this right. So he faces his problem alone; trapped between a pregnant lady and a hard place.
The real problem is that he is alone. So he does not see the true trap until it is far too late.