The problem is that => is just a comma, and if the lhs is a bare word it's automatically quoted.

So what you write is parse as $_, 2 * $_, 1..10, so 2 * $_ is the first item of the list.

$ perl -MO=Deparse -e 'my %foo = map( $_ => 2*$_, 1..10 );'
my(%foo) = map($_, 2 * $_, 1..10);
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In general terms an EXPR is everything that returns a value, but EXPR, LIST means that there has to be a decision where EXPR ends and LIST starts, and that's the first comma.