I recall an English teacher explaining that verbs that change vowels during tense changes were called 'regular' and those that added '-ed' in the past tense were 'irregular'. This seemed counter-intuitive, but the explanation was that early English verb conjugation regularly inflected a vowel rather than not. Is this correct?
It may be that your teacher was wrong, or it may be that one of you confused "regular" verbs with "strong" verbs.
In English linguistics (and Germanic languages in general), there are two classes of verbs known as the "strong verbs" and the "weak verbs". The strong verbs are those whose past tense and past participle are formed by ablaut, which is a vowel change in the stem of the verb. Strong verbs usually have a past participle which is different from the simple past form, and may have their past participle formed by -en.
The "weak verbs" are those whose past tense is formed with -d, -ed, or -t. These rarely or never have a past participle that's distinct from the simple past form.
In principle, this distinction is orthogonal to the regular/irregular distinction. As the previous examples show, there are both regular weak verbs (lift/lifted) and irregular weak verbs (say/said). In older forms of English there were both regular and irregular strong verbs as well, but as time has gone on the "regular" strong verb patterns have applied to fewer and fewer verbs.
As a result, in modern English all strong verbs are irregular, and all regular verbs are weak verbs. However, in Old English the strong verbs were more common than the weak verbs, and most of the strong verbs were considered regular verbs. This confusion between "regular" and "strong" verbs is probably at the root of what your teacher said.