The words airing, erring sound the same but have different meanings and spellings. Why do airing, erring sound the same even though they are completely different words?
The answer is simple: airing, erring are homophones of the English language.
the opening of a subject to widespread discussion and debate
the act of supplying fresh air and getting rid of foul air
a short excursion (a walk or ride) in the open air
A <xref>public</xref> <xref>expression</xref> of an <xref>opinion</xref> or <xref>discussion</xref> of a <xref>subject</xref>.
capable of making an error
Present participle of <xref>err</xref>.
Present participle of <xref>er</xref>.
capable of making an error.
Definitions from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved., from Wiktionary, Creative Commons Attribution/Share-Alike License., from the GNU version of the Collaborative International Dictionary of English. and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.