Is there a specific term for false justifications? I'm not sure "false justifications" is the right term, but it's the closest I can think of. I'm referring to a situation in which a person has already made up his mind for reasons he won't publicly disclose, then tries to justify using specious excuses that don't hold up under scrutiny.

For example, let's suppose a new manager wants to fire an employee for reasons that would be illegal. Instead, he comes up with a laundry list of legal reasons (tardiness, improper dress, poor attitude, lack of productivity). Taken as a whole and unexamined, the list seems overwhelming and thus the dismissal justifiable. But if given the opportunity, the employee could refute each reason individually (has never actually been late, dresses the same as others in the office, is meeting all quotas and agreements, etc).

Similarly, in political conversations a person's argument may be based on a conclusion driven by passions and beliefs, but not data. Then data is cherrypicked to prove the argument rather than forming an argument based on the data.

I'm looking for ways to describe this sort of pre-determination. Is there a language for this?
I think the examples refer to a variety of possible terms.

In cognitive science, there is much interest in cases where justification is triggered unconsciously.  The general tendency to justify one's decisions - especially the bad ones - is called self-justification:


  Self-justification describes how, when a person encounters cognitive
  dissonance, or a situation in which a person's behavior is
  inconsistent with their beliefs, that person tends to justify the
  behavior and deny any negative feedback associated with the behavior.


When someone makes a decision they know is bad, and uses rational-sounding excuses to obfuscate this, it is called rationalization:


  In psychology and logic, rationalization or rationalisation (also
  known as making excuses) is a defense mechanism in which
  controversial behaviors or feelings are justified and explained in a
  seemingly rational or logical manner to avoid the true explanation,
  and are made consciously tolerable – or even admirable and superior –
  by plausible means.


If scientific-sounding data is added to make a decision seem more objective than it is, then it is called intellectualization:


  Intellectualization is a defense mechanism where reasoning is used to
  block confrontation with an unconscious conflict and its associated
  emotional stress where thinking is used to avoid feeling.


Cherry-picking data to support an argument is an example of confirmation bias:


  Confirmation bias, also called myside bias, is the tendency to search
  for, interpret, prefer, and recall information in a way that confirms
  one's beliefs or hypotheses while giving disproportionately less
  attention to information that contradicts it.


A common view in psychology is that most explanations of decisions made are actually "post-hoc rationalization", or "post-rationalization" (see for example self-perception theory).

Sometimes justification is done consciously / intentionally.  The term you used, cherry picking, is perfectly valid in this case.  Another example is spin.