How does beta branching stop alpha helices from forming?
The answer to this, as said by @canadianer in comment, is that beta branched amino acids are bulky and can sterically clash with neighbouring atoms, forcing the backbone to adopt torsion angles which don't favour helix formation.

I couldn't find reference for these exact words, but similar one here:


  amino acids such as Valine, Isoleucine, and Threonine all have branching at the beta carbon, this will cause steric clashes in an alpha helix arrangement... valine, threonine, and isoleucine will often destabilize the helix because of branching of the beta carbon. These three amino acid residues are more often found in beta-pleated sheets, where their side chains will lie in a separate plane than the main chain.


Also, for torsion angles, from same source:


  The torsion angle is the measure in degrees in bonds between atoms. Folding of proteins are influenced by the degree of rotation amino bonds can hold. There are two different types of torsion angles existing in polypeptide bonds. Psi, ψ is the angle between the α-carbon and the nitrogen atom of a peptide bond. The other bond is called phi, φ which is the angle between the α-carbon and the carbonyl group.




See this table for details of which amino acid prefers which configuration:



Source