Why does Mochizuki insist on “forgetting the previous history of an object”?

What is the simplest (at the lowest level feasible) explanation of the approach of “forgetting the history” of a mathematical object,as used in Inter-universal Teichmüller Theory (IUTT)? Please explain:

• What are these operations and their history? (Without that we get nowhere!)
• How can an exposition or proof forbid the reader to use previous known information about an object? (This just sounds unreasonable to me.)
• What is a really simple example of a history with re-initialisation playing a useful rôle? (This would help one to understand and accept the method.)
• Is this method broadly accepted? (Scholze and Stix do not mention it in their reports², though it is evidently very important to Mochizuki.)

N.B.

• I am not asking what is the status of the purported proof of the abc conjecture, though that is obviously relevant.
• I admit to not having so much as started to try to study the IUTT papers³, but do not think that amounts to an unreasonable lack of effort to solve my problem myself, given that I understand that many professional mathematicians have shied away from them. I am hoping that someone else has at least got far enough to answer.

Background

Shinichi Mochizuki, initiator of IUTT,says in §5 of his report¹ of discussions with critics of IUTT that:

¡My précis!

The logical origin of the differences in viewpoint and so of misunderstandings by critics might be the different approaches to histories of operations on mathematical objects (e.g. structures):

Conventional: Conventionally, one regards all operations as parts of a single history, wherein they are all accessible.

IUTT: IUTT frequently uses re-initialisation operations— i.e. one “forgets” the previous history of an object, regarding it as inaccessible in subsequent discussions._{Re-initialisation necessitates labels for “before and after versions” of an object and explicit specification of the types (in IUTT: “species”) of objects, particularly before and after re-initialisation (e.g. “automorphism groups of fields” / “abstract topological groups”).}

References

¹_{http://www.kurims.kyoto-u.ac.jp/~motizuki/Rpt2018.pdf– Report by Shinichi Mochizuki of discussions in March 2018 between himself and Yuichiro Hoshi (expounding IUTT) and Peter Scholze and Jakob Stix (questioning its methods).}

• _{(see also other documents at http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTch-discussions-2018-03.html)}

²_{http://www.kurims.kyoto-u.ac.jp/~motizuki/SS2018-08.pdf (August 2018), critique by Scholze and Stix, one of the other documents referred to in ¹}

• _{(first draft: http://www.kurims.kyoto-u.ac.jp/~motizuki/SS2018-05.pdf (May 2018)).}

³_{S. Mochizuki, Inter-universal Teichmüller Theory (August 2012):}

_{I: Construction of Hodge Theaters, RIMS Preprint 1756
II: Hodge-Arakelov-theoretic Evaluation, RIMS Preprint 1757
III: Canonical Splittings of the Log-theta-lattice, RIMS Preprint 1758
IV: Log-volume Computations and Set-theoretic Foundations, RIMS Preprint 1759}