Why I cannot subdivide face in this way? I'm trying to subdivide a face using same technique I used in 3d max with no issues.

Here the steps:


I start with a cube removing 3 faces.





After I select the top edge of left face and I subdivide it (to have a vertex in the middle)





Do same operation with bottom edge of same face:





Select the already created top and bottom vertex and hit F:




Looks like the face has been divided in two but If I try to selected the left face I cannot:



Anybody could tell me why I cannot do it in this way?

Thanks.
When you subdivide this way, you're not subdividing a face, just one of it's edges.  Joining the new vertices up later with F still won't subdivide the original face.  

Have you tried selecting both edges together, then doing the subdivide?  This should split the face up into two. 

Select one edge, hold SHIFT down and select the other.
With both edges highlited, press W and do the subdivide.