When two creatures fight, they each deal damage to each other at the same time.
And any damage from a source with Wither (or Infect) dealt to a creature is dealt in the form of -1/-1 counters.
So if your Necroskitter were to fight your opponent's 3/3, then both would live. But the 3/3 would now have a -1/-1 counter on it, making it a 2/2.
In general, even if the spell or ability has two creatures, one of which has wither, deal damage to each other one after the other rather than by fighting (C.R. 701.12a), such as with Karplusan Yeti's ability, the creature with wither will cause -1/-1 counters to be put on the other creature this way (C.R. 120.3d), regardless of whether it deals damage first or second.
This is because state-based actions, such as the one that sends creatures with toughness 0 or less to the graveyard, are not checked while a spell or ability is resolving (C.R. 704.3, 117.2e, 704.5f, 608.2c, 117.3b, 117.5; see also C.R. 704.4).
EDIT (Apr. 29): Added rule citations.
EDIT (Mar. 8, 2021): Edited, including because some rules were renumbered in the meantime.
And any damage from a source with Wither (or Infect) dealt to a creature is dealt in the form of -1/-1 counters.
So if your Necroskitter were to fight your opponent's 3/3, then both would live. But the 3/3 would now have a -1/-1 counter on it, making it a 2/2.
This is because state-based actions, such as the one that sends creatures with toughness 0 or less to the graveyard, are not checked while a spell or ability is resolving (C.R. 704.3, 117.2e, 704.5f, 608.2c, 117.3b, 117.5; see also C.R. 704.4).
EDIT (Apr. 29): Added rule citations.
EDIT (Mar. 8, 2021): Edited, including because some rules were renumbered in the meantime.