Are all pathogens parasites?
Not all pathogens are parasites. Many opportunistic infections can be caused by organisms that are normally commensal or even mutualistic.
For example, this paper describes how multiple bacteria species can be pathogenic as well as mutualistic.

Despite its generally innocuous nature, over the past 20 years S.
epidermidis has emerged as a frequent cause of nosocomial infections.
Several extrinsic factors contribute to the conversion of S.
epidermidis from a member of the resident microflora to an infectious
agent. The bacteria primarily infect compromised patients including
drug abusers, those on immunosuppressive therapy, patients with
acquired immune deficiency syndrome (AIDS), premature neonates and
patients with an indwelling device.
...
Recent studies can be interpreted to suggest that S. epidermidis is a
mutualistic organism, much like the bacteria of the gut. Many strains
of S. epidermidis produce lantibiotics, which are
lanthionine-containing antibacterial peptides, also known as
bacteriocins (Fig. 3). Among the several identified bacteriocins are
epidermin, epilancin K7, epilancin 15X, Pep5 and staphylococcin
1580.37–39 Additional antimicrobial peptides on the surface of the skin have recently been identified as originating from S. epidermidis.
...
The removal of S. epidermidis (i.e. through overuse of topical
antibiotics) may be detrimental to the host for two reasons. Firstly,
removing S. epidermidis eliminates the bacterium’s endogenous
antimicrobial peptides, allowing potentially pathogenic organisms to
colonize the skin more effectively. Secondly, without bacterial
priming of the skin, the host may be less efficient in warding off
infection.