Why does commercial brown (whole wheat) bread taste bitter?
Much of the bitterness in breads made from whole wheat is caused by the phenolic acid and tannins in the bran layer of the wheat. Different varieties of wheat have different levels of those compounds and produce breads with different levels of bitterness. "Traditional" varieties of wheat, such as red wheat, contain high levels of tannins, while hard white spring wheat contains relatively low levels of tannins.

Here is what bakingbusiness.com has to say about this subject:


  With whole wheat, taste differences boil down to the tannin content of
  the bran. These red pigments in hard red wheat carry a bitter flavor.
  “... Whiter whole-grain varieties typically contain fewer tannins, which
  results in a less bitter taste,” said Brook Carson, technical product
  manager, ADM Milling, Shawnee Mission, Kansas. "Differences in taste can
  also be overcome with added sweetness or with a masking agent."


Based on your question, it sounds likely the Pillsbury Chakki Fresh Atta whole wheat flour you use for making parathas is milled from either hard white spring wheat or a blend of the white wheat with a more traditional variety of wheat resulting in a non-bitter end product. 

There is another possible source of bitterness in bread made from whole wheat flour, although it shouldn’t really affect commercially made bread. When whole wheat flour is milled, it includes the oil containing wheat germ, which is different than refined white flour where the wheat germ is removed prior to milling.  This oil in the whole wheat flour results in it having a much shorter shelf life than white flour and makes it susceptible to rancidity if not stored properly. Commercial bakeries go through (literally) tons of flour, so their whole wheat flour shouldn't be sitting around long enough to go bad.

I can tell you from first-hand experience, one of the signs whole wheat flour has started to go rancid is an increase in bitterness.