Starting in the 1400s, English vowels began a change known as the Great Vowel Shift, resulting in the change from English vowels being pronounced similarly to how the German vowels are pronounced now to how English vowels are pronounced today.
The diagram in that article explains the shift much more clearly and completely than I could, but the gist of it is this:
(Using the International Phonetic Alphabet):
- The vowel of time changed from [iː] to [aɪ].
- The vowel of see changed from [eː] to [iː].
- The vowel of east changed from [ɛː] and merged with the vowel see to become ultimately [iː].
- The vowel of name changed from [aː] to [eɪ].
- The vowel of day changed from [æj] and merged with the vowel of name to become ultimately [eɪ].
- The vowel of house changed from [uː] to [aʊ].
- The vowel of moon changed from [oː] to [uː].
- The vowel of stone changed from [ɔː] to [oʊ].
- the vowel of know changed from [au] and merged with the vowel of stone to become [oʊ].
- the vowel of law changed from [ɑu] to [ɔː]
- the vowel of new changed from [eu]/[iu] to [juː]
- the vowel of dew changed from [ɛu] and merged with the vowel of new to become [juː]
- the vowel of that changed from [a] to [æ]
- the vowel of fox changed from [o] to [ɒ]
- the vowel of cut changed from [ʊ] to [ʌ]
"Vowel spaces", that is, the system of vowels in a language and how they are arranged, are sensitive to changes in complex ways. When one vowel changes in how it is pronounced, due to normal language change, often several other vowels change at the same time, to keep the arrangement of the vowels in the vowel space "equally spaced". Such groups of changes are known as chain shifts. Keeping vowels evenly distributed in the vowel space avoids confusion as to which vowel was produced.