Rock paper chips - the scissors I mean secret counterstyles of Poker

If the four player types were pure and didn't combine with other types to make playstyle then the following would ring true:
So
A: LAG counters TAG
B: TAG counters LP
C: LP counters TP
D: TP counters LAG

Why?

A
The tightness preflop of the TAG lets the LAg frequently bully them off of hands but furthermore since they are sure to bet when hitting, at least by the turn card the lag has clear bluff stances to take advantage of regularly, even if the tag does raise their raise tends to be proportional to hand strength so even if they hit, big bets tend to throw them off frequently especially at the river if it's clear they don't have twopair or better.

B
This very obvious. While the LP will catch the TAG out by calling with very strong hands rather than raising, their looseness with starting hands and furthermore their lack of aggression to push off the TAG from also passively going to river card to outdraw them (such as flush outdrawing twopair) the LP is cornering themselves into consistently losing majority of hands where bets get big no matter what while against a TAG.

C
This seems to make no sense at first, how does a LP counter a TP? I mean if they really bet nothing at all and both remain totally passive then maybe neither style really wins as such but if we say they are passive in the sense they bet 2bb maximum even for huge strength of hands and that the only time the tp ever bets bigger than that is with near unbeatable nuts, the LP is going to begin to catch on and bet tiny bluffs that regularly the tp will cower away from as they never defend blinds, never fight when the turn is a high card than their flopped top pair etc. So if the two types use a tiny bit of aggression the lp is going to be making the tp regularly fold and have a perfect ability to judge them from the timing and frequency of their tiny bets on a hand (frequency as in flop turn and river all getting bets or bets stopping at turn or rover giving huge clues)

D
TPs are specialists in baiting, in fact even a brilliant TAG player can totally play into the hands of a sly TP now and again. LAGs however are countered by the TP because of inability to ever accurately know of a bluff can be pulled off. Assuming the TP is aware of the LAG being loose, may be willing to call bets that are small if they hit the cards in any way rather than only calling with pure nuts (which may be the only time they raise) so unlike with TAGs who make it so clear for the LAG when they are feeling weak, the LAG can rarely risk betting big against the TP in fear of that they will a pair the same as three of a kind and this means the TP is going to be dealing with small bets from a loose player which is going to most of the time mean they end up on top of they hit the flop etc with their high winds rate pocket cards.