I'll respond in more than one part, Minoosh; this is part 1.
This "for example" referred to accepting strange things about the universe. It's been agreed upon by many that QM is strange. Perhaps a synonym could be "counterintuitive." The "spooky action at a distance" of entangled photon pairs might be a good example.
Have you heard of "lies to children" (
WP)?
Briefly, it's the idea that when we try to explain something to children, we tend to be very brief, and omit some key aspects. As you go through school, college, and university, you realize that a great many of the things your parents, teachers, and lecturers told you were not entirely correct, and some even "lies".
QM is both the most successful of modern physics ideas (in many respects), and the most difficult to grasp, intuitively. And perhaps nothing in QM is harder to grock than the so-called "'spooky action at a distance' of entangled photon pairs".
You can see, in this thread and the other, the willful deceit of Danielscience in action, on this (and some broader aspects). But even the very popular Dr Nye, the Science Guy gets it wrong (see Backreaction's "Hey Bill Nye, Please stop talking nonsense about quantum mechanics."
link).
In high school physics I got a decent grounding in Newton's laws. Given an ellipse I could derive the formula and given the formula I could plot an elliptical orbit that corresponded with what I knew about the inverse-square property of gravitational attraction. But I knew that didn't scale down to the size of an atom; electrons do not orbit the proton as the Earth orbits the sun. Do they?
Correct.
The 'solar system model of the atom' is an excellent example of a lie to children.
Once you learn that accelerating charges emit electromagnetic energy (Maxwell's equations), you realize that this model cannot possibly be correct (if it were, every electron in every atom would spiral into the nucleus in less than a nanosecond) (FWIW, the internet is drenched with woo like the Electric Universe, and apparently many of their hard core believers are unaware of this, despite 'electricity' being at the core of their beliefs

).
I've watched the BBT too and "the whole universe was in a hot dense state" doesn't begin to capture the WOOOMPPHHH! that must have been required to blow something the size of a pinhead (if that; a cosmologist once told me "smaller than a proton") into this universe.
Sadly, this is yet another 'lie to children'. Several actually.
The "Big Bang" was not an explosion in the sense that we are familiar with (i.e. an explosion
in space); rather it was a rapid expansion
of space (to be as brief as I can). This confusion may be partly responsible for the ridiculous Danielscience argument against it, i.e. that even primary schoolkids can refute GR (a crucial element of the BBT) by pointing out that "time cannot bend".
Second, it isn't "the whole universe" that was the size of a pinhead (or a proton), it's the
observable universe. Again, this is not easy to grasp, but the BBT leaves quite open what's 'beyond' the observable universe, including whether it's infinite.
Beyond the Universe is a good, recent blog post on this.
Third, the BBT ends with the mutual incompatibility of QM and GR being so severe that models break down.
And since the thing had a beginning I'm still stuck on the question: "What about before the beginning?"
Indeed.
This is one of the most widespread lie to children, re the BBT. The physical regime in which QM and GR are severely mutually incompatible is called the Planck regime. With some perhaps unwarranted extrapolations, models of the universe can 'go back' to a hot dense state that is just outside this regime. No model can 'go further', unless it incorporates a model of quantum gravity. There are several such, in the physics/cosmology literature (i.e. journal papers), but none has yet been adequately tested.
So, in the BBT there is no "beginning", nor any statement whatsoever about an origin; rather an honest "no one knows, yet".
Ned Wright has a good
Cosmology Tutorial that might be at a level suitable for you; it tries to avoid any lies to children.
For this reason I have some patience with creationists.
I guess I might have some too ... but for the obvious willful deceit, the arrogance, and so on. I mean, isn't the book they seem to like so much replete with exhortations to be humble? to not willfully lie? Did they not read this book?
(more later)