As a physicist, I believe that the many-world interpretation of quantum physics is the best because it is more practical than its competitors.
The first major competitor is the theory that the world is deterministic and its just our lack of knowledge that causes us to perceive a non-deterministic world. The problem with this is that we have no evidence in favor of this proposition and to the extent we have any evidence it is *against* this proposition.
The other major competitor is the theory that the wave function of the whole universe collapses every time we make a measurement. This agrees very well with experiment as long as the person asking the question is the one doing the measurement, but it has a major problem: since wave functions don't collapse unless measured, what counts as a measurement? For example, does collapse only happen when *I* make a measurement? If so, why should I be uniquely privileged? Alternatively, does collapse happen whenever some human being makes a measurement --- that is, if I perform the Schroedinger's cat experiment but with a person instead of a cat inside the box, then has the wave function collapsed even if I never open the box (assuming it is perfectly insulated)?
The advantage of the many-worlds interpretation is that it solves the problem of measurement by *not* treating measurement as being an special-case exception to the rules; it postulates that the wave function of the universe never actually collapses. Given this, how do we make sense of the fact we human beings *do* observe such a collapse? The answer actually appears right in the math: when we demand that a particle in a mix of states tell us which state it is in, it causes us to become entangled with the particle so that a *portion* of the universe splits into two states: one with the particle in the first state and us seeing it in the first state, one with the particle in the second state and us seeing it in the second state, and so on. So from the perspective of each of the observers the wave function has collapsed even though it never did. What happens then if you put an observer in a box and have him or her make a measurement? The answer also appears in the math: although the universe splits inside the box, it does not split outside the box.
This might seem fanciful, but it is something that we can actually test. Although we cannot put human beings in a box for ethical reasons, we can put increasingly large systems in the box that act as "observers" of some particle (by engineering an interaction between the observer and the particle) and then perform interference experiments to determine whether the wave function in the box has collapsed or not. Every such experiment we have performed has shown that the wave function does in fact *not* collapse inside the box but rather splits.
So what is the mathematical difference between being inside the portion of the universe that splits and being outside it? It is simple: if you are outside the portion that splits, then the wave function of the universe can be expressed as a tensor product between you and splitting portion. If you are inside the portion that splits, then this can never be the case.
Thus it turns out that measurement *already falls out of quantum mechanics* in a mathematically rigorous and observer-independent fashion, as long as we are willing to accept that a consequence of this is that from the view of someone external to the universe there is a (mathematically rigorous) sense in which there are multiple copies of you and I within the universe. Sure, if we don't like this consequence we can add a rule that gets rid of it by specifying that the wave-function collapses, but then you have to introduce some arbitrary rule that specified that some macroscopic bodies have the power to cause a collapse but not others. Now in fairness, there do turn out to be mathematically rigorous ways to do this and some of them even provide testable predictions so one of them might be proven correct one day, but there is no evidence that any of them is correct and again all of our experiments to date have indicated that if the experimenter is isolated from the observer than the wave function does not collapse under observation so I am not holding my breath.
In conclusion, speculating about which interpretation of the world is correct is actually not pseudoscience because many of the competing interpretations have quantitative characteristics that we can explore using mathematics and probe using experiments.