Microeconomics is almost a branch of psychology, because it is fundamentally about behaviour

and:

Macroeconomics, on the other hand, is like thermodynamics. It deals with economic systems so large that the specific details of the economic behaviour of individuals are irrelevant

Are pertinent.  I think your observation that microeconomics is almost a psychology is exactly right.  However, I strongly disagree with your conclusion about macroeconomics, even though I believe your supporting statements about individual behavior being irrelevant, etc., to be correct.

I think with macroeconomics, what we're witnessing is group psychology and behavior.  In these fields, individual behavior and predictions are next to impossible while large groups tend to act predictably.  Thus, it is tempting to think of it as a science which can be mathematically explained.

But that's very wrong.  The seeming stability of macroeconomics is explained by group behavior and things like disbursal of responsibility which make larger groups more stable than smaller ones.

The key difference is that the laws of thermodynamics will still exist even if everyone in the world stops believing in them.  The same cannot be said of the economy.  You're correct that individual behavior has little effect, but group behavior does.

Maybe we can eventually make language a complete impediment to understanding. -Hobbes

There is an evolutionary reason to expect that behavior will, at least, not reflect cyclic preferences. If preferences run A > B > C > A, then no utility function can be found -- but a game player with these cyclic preferences can be exploited: trade B for C plus a side-payment, then A for B, then C for A. Repeat, and extract value from the cyclic player for free. The exploitability of cyclic preferences drives evolution (genetic and cultural) toward eliminating them.

(On the other hand, transaction costs and refusal to play certain games should be enough to protect some cyclic preferences from exploitation, which reduces the consequence of this result.)

The above description of classes of preference structures will, however, seem to be more-or-less complete only if one falls into the fallacy of treating "fully ordered" and "unordered" as the only sorts of order. This of course neglects partial orders: for example, models based on Pareto optimality. The preference aspect of partially ordered preferences can be described by many utility functions, but their indifferences (or non-preferences) cannot be so described. Because partial orders lack cycles, they are immune to exploitation of the sort described above, yet they are not strong enough to support some arguments that go through in the case of full orders. Utility functions are just too strong.

Utility functions for groups are of course quite problematic and strongly motivate the use of Pareto orderings. Schelling argues that an "individual" mind is in fact divided in ways that make it more like a group, which motivates his application of game theory to purely personal choices and may explain some of the deviation of human behavior from utility-based models.

Saunders Mac Lane observes (and I agree) that neglect of the concept of partial orders is a major source of erroreous thinking in the social sciences, even beyond mathematical economics.

Words and ideas I offer here may be used freely and without attribution.