If you got a minute,
https://youtu.be/f_8myEDBD9Aand then also
https://youtu.be/eeLa9tIhFMs(minimal logic is the logic without excluded middle nor explosion)
Explosion is a simple consequence in arithmetic (where you just need to reduce a false numerical statement to 0=1, which then gives you all equations), but otherwise it's more difficult to motivate.
The next best "clearly sensible" principle is the disjunctive syllogism: If "A or B" is proven and if "not B" is established too, then "A" must be the case. Now considering B for A, we get that A and not A gives A. And that works for any A. So, if we adopt this principle, then at least any statement that's a proven inconsistency follows.
If we adopt the weakening principle of the Disjunction, we get explosion. The weakening of an established statement "A" is that then "A or B" is also true (weakening since claiming "A or B" is giving less information than claiming "A"). With this, given any established inconsistent statement C (i.e. we have both C and not C), we can form "C or A" and then get A by the disjunctive syllogism.
All of this is formal logic and you may contest any of those statements. E.g. in relevant logic, Disjunction and implication aren't allowed to relate semantically unrelated statements (e.g. the colors of sky and grass, as in the third post)
