I apoligize that this question is not very formalized. Maybe the assumption in the question is wrong. I am asking because looking at latin, greek and sanskrit, these languages seem quite similar to eachother, where as the germanic languages seem quite different. The former have retained a lot of the case, gender and verb structures from PIE. Proto-germanic seems to have had this, but none of the modern germanic languages have these at all. Except icelandic and to a lesser degree german, but dutch, english, the scandinavian languages don't use case except a little in pronouns. Phonologically other PIE languages seem more similar as well. I realize this is not very rigorous, but when i listen to reconstructions of PIE read aloud, it sounds much more like a romance language than a germanic one. Again, sorry if this question is stupid, I know next to nothing about linguistics.
I wouldn't say Germanic languages are particularly unique in the fact that they heavily diverge from PIE. Every branch of the Indo-European language family has made innovations that rival those of Germanic. That having been said, Germanic languages have made a couple of innovations that tend to stand out among IE languages, at least anecdotally in the personal opinions of speakers of those languages.
Phonologically speaking, Germanic languages are unique in the development of fricatives out of the PIE voiceless stops, part of a chain shift known as Grimm's Law. Another shift known as Verner's law then voiced these fricatives after unstressed syllables, creating 8 new phonemes (*ɸ *β *θ *ð *x *ɣ *xʷ *ɣʷ). Germanic a-mutation, umlaut, and various u-mutations in Germanic languages such as English complicated the vowels of Germanic languages to a similar degree.
As noted in another answer, Germanic languages simplified the complicated PIE stress system into uniform initial stress, which then caused the erosion of grammatical inflections inherited from PIE. PIE was a very highly inflected language, so it is no surprise that the trend of most of its daughter languages is to reduce inflectional complexity. While the Germanic languages are perhaps particularly far along in this trend, many others aren't far behind. The Western Romance languages have lost case entirely and similar stress patterns are simplifying verb conjugation, particularly in informal speech. Indo-Aryan languages such as Farsi, Kurdish, Ossetic, and Bengali have lost grammatical gender, which is still around in most Germanic languages.
It's also important to note the time difference between the earliest attestations of each branch. By the time we find our first text in a Germanic language (Gothic, ~300s CE), Latin, Ancient Greek, and Sanskrit had been around for hundreds of years, and were nearing the ends of their lives as spoken languages. Because these older languages have less time separating them from PIE, it follows that they would be more similar to it.
At the end of the day, as much as the Germanic languages innovate, they can also be conservative. Most point to English as being very unlike PIE, but interestingly it is to my knowledge the only living IE language to have entirely conserved the PIE semivowels word-initially (PIE *yugóm -> yoke, PIE *weh₁iros -> wire).
The Germanic languages in their earliest documented stages (specially Gothic) aren't too different from the other family members. However, initial stress started to erode the delicate system of endings, resulting in typologically quite different languages, shifting from inflecting to isolating type. So the most disrupting event in the history of Germanic languages was the acquisition of word-initial stress.