The most important resource with regard to Albert Einstein's biography are Princeton University's Collected Papers. Particularly relevant to the question is John Stachel (ed.), The Collected Papers of Albert Einstein, Volume I: The Early Years 1879-1902, Princeton University Press 1987. In this we find excerpts from a biographical sketch written by Einstein's younger sister Maja in 1924:
Maja Winteler-Einstein, "Albert Einstein — Beitrag für sein Lebensbild", pp. xlviii-lxvi
In 1894 the electrotechnical company of Einstein's father and uncle suffered business failure, and based on a suggestion by an Italian friend the Einstein family moved to Milan in Italy to try and rebuild their lives there. 15-year old Albert was left behind in Munich to finish high school. He had been enrolled at the prestigious Luitpold-Gymnasium since 1887. Winteler-Einstein writes (p. lxiii):
Besonders unangenehm war dem Jungen auch der militärische Ton in der Schule, die systematische Erziehung zur Verehrung der Autoritäten, die bereits die Schüler an die militärische Zucht gewöhnen sollten. Mit Grauen gedachte er der nicht mehr allzufernen Zeit, da er den Soldatenrock anzuziehen hatte, um seiner Dienstpflicht zu genügen.  Seelisch bedrückt u. nervös geworden, sucht er nach einem Ausweg. Als daher der Ordinarius der Klasse ihn bei irgend einer Gelegenheit hart anliess (es war derjenige, der ihm prophezeit hatte, dass nie etwas rechtes aus ihm werden würde), liess er sich vom Hausarzt ein Zeugnis geben, wies es dem Schuldirektor vor u. reiste
kurzentschlossen nach Mailand zu seinen Eltern.
My translation: "The military tone at the school was particularly objectionable to the boy, the systematic education to venerate authorities designed to accustom already students to military discipline. With utter dread he thought of the not too distant time when he would have to don a soldier's uniform to comply with his [military] service requirements. Emotionally depressed and nervous he looked for an escape route. Therefore, when his home-room teacher spoke to him harshly at some occasion (it was the same one who had pronounced that he would never amount to anything), he obtained a doctor's note from the family physician, showed it to the school's principal, and shortly departed to his parents in Milan."
At that time all German males from age 17 to 45 were "wehrpflichtig", that is, subject to military conscription and were called up for compulsory military service between ages 20 and 39. As an additional requirement young males age 16 or older had to obtain permission from the government before leaving the country, presumably to prevent draft dodging by temporarily moving abroad. Einstein was about 15¾ years old when he left Germany. Einstein was a pacifist who abhorred all things military [*]. Two footnotes to Winteler-Einstein's text make clear Einstein's perception of his teachers:
 Einstein reportedly said: "Die Lehrer in der Elementarschule kamen mir wie Feldwebel vor und die Lehrer im Gymnasium wie Leutnants" (Frank 1979, pp. 24-25, see also Moszkowski 1921, p. 221)
 [...] Einstein later spoke of his Gymnasium teachers as "überwiegend dem Leutnants-charakter zugewendet" [Moszkowski 1921, pp. 221)
These say that "My teachers in elementary school seemed like [drill] sergeants to me, and the teachers in the Gymnasium like lieutenants" and most of his high-school teachers "adopted the character of lieutenants".
I see no evidence of Einstein being expelled from (kicked out of) the Luitpold-Gymnasium, but a further footnote indicates that his home-room teacher had expressed the desire for him to leave the school:
 "Als ich in der 7. Klasse des Luitpoldgymnasiums war, liess mich der Klassenlehrer [Joseph Degenhart] kommen und äusserte den Wunsch, ich möchte die Schule verlassen. Auf meine Bemerkung, dass ich mir doch nichts hätte zuschulden kommen lassen, antwortete er nur: Ihre blosse Anwesenheit verdirbt mir den Respekt in der Klasse" (Einstein to Philipp Frank, draft letter, 1940). He withdrew from the school on 29 December 1894 (Jahresbericht München 1895, pp. 27, 28).
My translation: "When I attended the 7th grade at the Luitpold-Gymnasium my home-room teacher called me in and expressed the desire that I should leave the school. When I remarked that I had done nothing wrong, he just replied: Your presence alone ruins the respect I receive in class."
[*] In Albert Einstein, "Mein Weltbild", Amsterdam: Querido Verlag 1934, he famously stated (I found some indications that this may have appeared in his writings as early as 1930):
Wenn einer mit Vergnügen in Reih und Glied zu einer Musik marschieren kann, dann verachte ich ihn schon; er hat sein großes Gehirn nur aus Irrtum bekommen, da für ihn das Rückenmark schon völlig genügen würde. Diesen Schandfleck der Zivilisation sollte man so schnell wie möglich zum Verschwinden bringen. Heldentum auf Kommando, sinnlose Gewalttat und leidige Vaterländerei, wie glühend hasse ich sie, wie gemein und verächtlich erscheint mir der Krieg; ich möchte mich lieber in Stücke schlagen lassen, als mich an einem so elenden Tun zu beteiligen!
My translation: "If someone can enjoy marching in rank and file accompanied by music I already despise him; he received his large brain only by accident as the spinal cord would be fully sufficient for him. This disgrace to civilization should be abolished as soon as possible. Heroism on command, senseless violence, and vexacious nationalism, how ardently I hate them, how mean and despicable war appears to me; I'd rather be hacked to pieces than participate in such base activity."