To a certain extent you are right as how can a Rebbi, a 'lowly' human being be on a level of a more heavenly-based מלאך? Surely it is impossible for a man that is essentially ‘earthly’ in form, to draw parallels with a celestially-rooted מלאך?
The answer is that just as a מלאך has no personal aspirations but rather is driven purely to satisfy the will of Hashem, so too a Rebbi must be focused entirely on fuelling the success of his תלמידים. (See HaRav Michel Yehuda Lefkowitz זצ"ל in קונטרוס יסודות החינוך מרבותינו גדולי ישראל שליט"א: דברים שנאמרו בכינוס מאות מחנכים ומנהלים רוחניים, כסלו תשע"א, 'הרב הדומה למלאך שכל כוונתו תועלת התלמיד', עמוד 5)
Thus, a Rebbi must be consistent with his appointed title. This means that he must not be deficient in the traits necessary for a מחנך. If a teacher is lacking in his level of observance, character or learning it will serve to hamper his personal example. Failure to be a true role model will abjectly impact on his students. (Refer to משנה תורה, הלכות תלמוד תורה ב:ג. The רמב"ם writes there; "לפיכך אין ראוי להושיב מלמד אלא 'בעל יראה' וכו'" – “Therefore, it is not fitting to appoint a teacher unless he is a G-d fearing person”.)
The fact that we liken our Rebbeim to angels is a testament to the high regard with which we view them. They serve to mould and fashion our children into 'עובדי ה, and for this alone, we must endeavour to ensure that our children receive the correct level of teaching. Indeed, Rabbi Moshe Shternbach שליט"א notes that one must be quick to ascertain that their children have a רבי who is a ירא שמים and this means seeing him with your own eyes to verify if he will provide a good example. (See ספר אורחות הבית, חלק ראשון, פרק ששה עשר, אות ז', עמוד קכב. He writes, "והיו עיניך רואות את מוריך היאך הוא מתנהג באורחות חייו וכשהוא מתפלל שיהא לדוגמא ומופת לתלמידיו" – “And your eyes themselves should see your teacher, how he acts in his daily life and when he davens he should be an example and source of wonder to his students”. In a similar vein, the חפץ חיים adds: "מאד מאד יתחזק האדם לראות שבנו ישיג חינוך טהור בידיעת התורה והמצות וכמו שנהגו אבותינו מלפנים בדרך החינוך ללמד את בניהם חומש ורש"י שיהיו עי"ז יהודי נאמן לד' ותורתו" – “It is highly important for a person to see that his child receive a pure chinuch with Torah knowledge and Mitzvos, and like our fathers before them were accustomed in the ways of chinuch to teach their children Chumash and Rashi, and through this, a Jew will believe in Hashem and His Torah”. As written in בית ישראל, מאמר לכלל ישראל)
Ultimately, in order for a teacher to positively influence others, it is an obligation on them to first fill themselves with יראת ה' and only then can they influence others. (ומצדיקי רבים, פרק א', 'ירא שמים',עמוד ג)
Rabbi Yaakov Neiman זצ"ל in his דרכי מוסר also explains how important it is for a teacher to be a ירא שמים. When an educator has this מדה his influence is all the more impactful on his תלמידים. For example, when a teacher relates the miraculous experiences of יציאת מצרים, and his absolute 'אמונת ה is evident, it enters into the heart of his students and leaves a lasting impression. (See 'דרכי מוסר, פרשת יתרו, 'והגדת לבנך. He begins by asking why it was that יתרו was so excited by משה’s report of the miracles that had occurred in the build up to and during יציאת מצרים, when he had already heard the same account prior? R’ Neiman answers,אינו דומה שומע מפי הרב לשומע מפי התלמיד תלוי מי המשמיע – “One cannot compare hearing something from the mouth of a Rov to hearing it from the mouth of the student, as it is dependent on the speaker.” This means that it was only when יתרו heard the miraculous happenings of מצרים from משה that it left a lasting impression.)
Conversely, when a teacher says something that lacks conviction, his students will see this lackadaisical approach and will not absorb the message. For this reason, R’ Neiman writes elsewhere that it is crucial that a Rebbi teaches with a mindset that is completely לשמה (See 'דרכי מוסר, פרשת תרומה, 'אחריות של המורה והמחנך). It is only when an act is performed לשמה that Hashem can allow His שכינה to settle. This is because when a person is of pure heart and mind; his resulting actions truly reflect his intentions. This purity consequently provides a foothold for the Divine presence to cling to. This means that teachers have a tremendous responsibility as when they avoid acting in a לשמה manner their students may not learn properly. This in turn, can result in disinterested students which can ח"ו leave them open to foreign and evil influence.
In both cases R’ Neiman brings the story of אלישה בן אבויה, the point you raised in the first part of your question who became known as אחר, a once leading Torah sage, who became an apostate and is since referred to as "אחר" (literally; “the other one”). Quoting תוספות on מסכת חגיגה ט"ו in the name of the ירושלמי, R’ Neiman relates how אחר believed himself to be doomed to failure from the outset. תוספות comments that אבויה was one of the great men of ירושלים, and on the day of his son’s ברית he invited all the distinguished men of the city to sit in one room and ר' אליעזר and ר' יהושע to sit separately in another room. After the dignitaries had eaten and drunk, they sang songs and did alphabetical acrostics. Seeing that the men were engaging in interests of theirs, ר' אליעזר and ר' יהושע felt that such action justified them occupying themselves with their own interest, namely, תורה study. They started with תורה, moving on to נביאים and then כתובים. Such was their enjoyment that fire descended from heaven and surrounded them. Upon seeing this phenomenon, אחר’s father remarked that due to the evident might of תורה, if his child would survive, he would dedicate his child to תורה. Thus אחר concludes, since his father’s intention was not לשמה the study of תורה did not endure for him. We learn from this story how important it is to have correct and heartfelt intentions. As seen by the case of אחר, failure to act in way that is לשמה can have catastrophic results.
Thus in short, the imagery of teachers as angels is not alluding to be something that they cannot be, but rather symbolic of an aspiration to provide an example that serves to inspire those under their charge. They should be יראי שמים and בני עליה which in turn, will no doubt serve to inspire their תלמידים and make them positive role models.