Join order - order in which joins are performed.

Why does driving off table B retrieve col1 while driving off table A *does not* retrieve col1 from their respective tables?

See below, in bold.

"FAQ: Interpreting Explain Plan

Join order - order in which joins are performed

The join order makes a significant difference to the way in which the
query is executed. By accessing particular row sources first, certain
predicates may be satisfied that are not satisfied by with other join orders.
This may prevent certain access paths from being taken.

e.g. Suppose there is a concatenated index on A(a.col1,a.col2)
     Note that a.col1 is the leading column.