Wolverine and Spider-Man have been allies for a long time, but one of the areas where they have sometimes been out of sorts with each other has been within the world of espionage (Spider-Man's parents, Richard and Mary Parker, had been spies for S.H.I.E.L.D. who had been killed on a mission when Peter was just a boy). Back in the 1980s, Peter Parker was on assignment for the Daily Bugle covering a spy that multiple agencies were trying to hunt down, and Peter got caught up in a deadly hunt for the spy, who turned out to be a friend of Wolverine's. Spider-Man fought with Wolverine at the time over Wolverine manipulating Spidey, and in the process, Spider-Man accidentally killed the aforementioned spy (she intentionally threw herself in front of Spider-Man's fist, as she WANTED to die to avoid being killed via torture by the agencies hunting her). It messed Spider-Man up, as you might imagine.
Wolverine and Spider-Man are teaming up again in a new ongoing series, Spider-Man and Wolverine, and this team-up involves spy secrets, as well, and in an CBR exclusive preview of next week's Spider-Man and Wolverine #2, we see that one of the revelations is driving Spider-Man into wanting to KILL Wolverine!
Spider-Man and Wolverine #2 is from writer Marc Guggenheim, artist Kaare Andrews, colorist Brian Reber, and letterer Travis Lanham, and it picks up from where the first issue left off, with Spider-Man discovering an old video that showed Wolverine, then working undercover for the Red Skull, seemingly murdering Peter's parents!

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A Shocking Revelation Turns Friends Into Enemies in Spider-Man and Wolverine #1
In a CBR review of Spider-Man and Wolverine #1, discover the shocking secret that might turn our heroes against each other
SPIDER-MAN & WOLVERINE #2
MARC GUGGENHEIM (W) • KAARE ANDREWS (A/C)
HIDDEN GEM VARIANT COVER BY HUMBERTO RAMOS
VARIANT COVER BY ERIK LARSEN • VARIANT COVER BY IBAN COELLO
VIRGIN VARIANT COVER BY KAARE ANDREWS
SPIDER-MAN VERSUS WOLVERINE!
You read that right! The inaugural issue’s surprise leads to this throwdown for the ages: SPIDER-MAN VERSUS WOLVERINE! But what terrible revelation could possibly pit PETER PARKER against LOGAN for all the marbles? Not mind control, not an illusion – you’ll have to read it to experience it!
32 PGS./Rated T+ …$4.99

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In the preview pages, Spider-Man ferociously attacks his would-be ally, and Wolverine is stunned to suddenly be on the defense against Spider-Man, as Spidey shouts at Wolverine that he killed his parents. Wolverine is still out of it, as Peter pummels him. We then see more details of the video recording that Spider-Man saw, which was part of a major data breach. It certainly appears as though Wolverine was assigned to kill Peter Parker's parents, Richard and Mary Parker.
However, the video does not show the entire story, so it is possible that there are more to things than what meet the eye, and you'll have to pick up a copy of Spider-Man and Wolverine #2 next week to see if that is the case or not (and whether Wolverine can prevent Spider-Man from, you know, killing him).
Source: Marvel