Chagigah 15b, in the context of relating how Rabbi Meir learned Torah from Acheir, states:
מאי דכתיב (מלאכי ב, ז) כי שפתי כהן ישמרו דעת ותורה יבקשו מפיהו כי מלאך ה' צבאות הוא אם דומה הרב למלאך ה' צבאות יבקשו תורה מפיהו ואם לאו אל יבקשו תורה מפיהו אמר ר"ל ר"מ קרא אשכח ודרש (משלי כב, יז) הט אזנך ושמע דברי חכמים ולבך תשית לדעתי לדעתם לא נאמר אלא לדעתי רב חנינא אמר מהכא (תהלים מה, יא) שמעי בת וראי והטי אזנך ושכחי עמך ובית אביך וגו' קשו קראי אהדדי לא קשיא הא בגדול הא בקטן
'What is [the meaning of] the verse, 'For my lips, a priest shall guard; knowledge and instruction they shall ask from his mouth, for he is an angel of Hashem of Legions (Malachi 2:7)'? If the teacher is like an angel of Hashem of Legions, they should ask instruction from his mouth; And if not, they should not ask instruction from his mouth.'" Reish Lakish said, "Rabbi Meir found a verse and expounded it: 'Incline your ear and hear the words of the wise ones; and put your heart to my knowledge (Proverbs 22:17).' 'To their knowledge' was not said, but rather 'to my knowledge'." Rav Chanina said from here: "Listen, daughter, and see, and incline your ear and forget your nation and your father's house... (Psalms 45:11)." The verses contradict each other! There is no contradiction. This one (ie. when there is no need for a teacher like an angel) is with an adult, and this one (ie. when there is a need for a teacher like an angel) is with a child.
From my personal experience, I know that, while the teachers at my school were very good, only one or two of them seemed to be without imperfections-- and they probably, somewhere along the line, where not perfectly Malach-like.
What is the heter for our chinuch institutions to hire people who aren't of angelic perfection to teach Torah to minors? Is it out of necessity, or is there a different/additional reason?