Was Metallica really responsible ?

People forget or don't know altogether what kind of an impact some songs had in the metal community. Songs like Whiplash were a huge shock and I think it is obvious that it is a song far heavier and faster than anything Venom did at that point.

Motorhead and Venom are definitely the godfathers of thrash (and Venom is also the godfather of death metal and black metal) but their music cannot be labelled thrash except in the case of a couple of songs (usually cited as proto-thrash).

In the Bay Area there were other bands doing heavy, fast music (like Exodus or Metal Church) but Metallica was the best and the first to set the standards. Slayer, as already mentioned had to take their cue from Metallica to step up their game after seeing them live in 1983 and still, you can't say that Hell Awaits was heavier than say Fight Fire with Fire or Creeping Death. Scarier, sure. Darker, absolutely. Sicker, of course! But heavier? Slayer sat on the thrash metal throne in 1986 with Reign in Blood but that's because Metallica were aiming for a much larger one (well, I am not sure they could dethrone Slayer even if they tried though... I mean Angel of Death and Raining Blood can't really be topped...).

Damage Inc, Battery, Disposable Heroes are absolute heavy as fuck and fast as hell thrash metal songs. Megadeth's classic Peace Sells is notably lighter and Anthrax were on the same level. Exodus? After the monumental Bonded by Blood, if anything got more accessible by thrash metal standards.

And it should be good to remember that the Big 4 of thrash had nothing to do with "first" or "most influential", even though they were certainly among them. It was all about the most popular and believe it or not during the Clash of the Titans tour (91), Slayer was the LEAST popular even though by that time they were the undisputed kings of thrash.

As for Mustaine's influence, he sure had a hand in shaping thrash metal from the start but the heaviest songs (like Whiplash, the final part of No Remorse, Motorbreath, the Hit the Lights riff) weren't his with the exception of Metal Militia. He wrote Jump in the Fire, Four Horsemen (as Mechanix) and Phantom Lord which are the closest to "traditional" heavy metal. His statements that he created thrash are really self-flattering as he always mentions the solos as being an integral part of it. Hetfield was way more responsible and it can be confirmed with the host of GBH and Discharge shirts he was seen wearing afterwards. He did not know those bands before Kill Em All was released but it is telling that he really appreciated the other extreme stuff of the time. 

Also let us not forget that Dave Mustaine was calling Megadeth the state of the art speed metal band, he wanted to be the fastest and the most technical (and certainly faster and more technical than Metallica, to prove a point).

Anthrax is VERY influential. Perhaps some don't like the kind of influence they had but it is undeniable. For starters, SOD was a HUGE influence to the groove/nu/rap/modern/whatever metal. How many bands have ripped off March of the SOD? That's 1985! The crossover, the image, the skate culture, the I'm the Man single which catapulted them to success, their tour with Public Enemy (unheard of! hip hop and thrash metal?). They really sold more than Slayer. As did Megadeth. 

There is a nice story about all that during the Clash of the Titans tour, when Mustaine was wondering why Slayer got to co-headline (and thus play last some nights) since they were clearly less popular than both Megadeth and Anthrax. And Scott Ian kinda agreed with that. Then famously, Slayer blew both bands out of the water on stage and in the merch sales, which resulted to the other two asking them to play last every night because otherwise the crowd was too exhausted for their shows. And again, famously, Kerry King was saying "serves them fuckers right, they wanted to rotate, we'll rotate!"

Good times. The least popular thrash metal band out of the big 4 destroying live the other two. Metallica of course in 1991 were on a completely different level.

I don't understand why people think Anthrax is the worst of the big four often, they are very underrated. Anthrax is my personal favorite of the big four.  

They were very important in the development in thrash and speed metal, just listen to Spreading the Disease.

I agree, I'm not too big on the John Bush-era either. I did love 'We've Come for You All' though. I know everyone has their own preferences, I've just never understood why Anthrax gets the least notice of the big four