Deniability properties of the X3DH Key Agreement Protocol Signal's X3DH Key Agreement Protocol specification states in section 4.5.:


  Alternatively, it might be tempting to replace the DH-based mutual authentication (i.e. DH1 and DH2) with signatures from the identity keys. However, this reduces deniability, [...]


How exactly does replacing DH1 and DH2 with signatures reduce deniability?
I think, using of signatures means something like STS protocol (https://en.wikipedia.org/wiki/Station-to-Station_protocol).
In STS, for the purpose of mutual authentication, 
each party must send a signature of ephemeral keys.
So, in terms used in https://signal.org/docs/specifications/x3dh ,
Alice should sign EK_a || SPK_b, and Bob should sign the same.

In X3DH, authentication provided by signatures is substituted by 
the fact that for getting the key (SK) each party should execute DH exchange using his identity key (say, ID_a) and counter-party's ephemeral key (say, SPK_b). So, in fact, signing of SPK_b with private key of ID_a (in STS) is substituted with just running of DH for ID_a and SPK_b (in X3DH).

So, what's the difference for deniability? Very simple: signature is evidence of communication and knowing of ephemeral keys, and hence knowing of SK. While running of DH is not an evidence, because it's even impossible to know wether Bob (or Alice) run DH and get SK or not.
If Alice will want to prove to some judge that Bob communicated with her,
and Bob knows some SK (and hence - he could create or at least decrypt some cypher-texts provided by Alice to judge), she can't prove it:
it's obvious that Alice could simulate DH with any EK_a key she wants. There's no evidence that Bob was running DH with EK_a and even know about existence of such EK_a.