While Quirrell could have asked Harry to help him as a friend, it would have risked Harry balking at any step in the process which involved sufficiently unethical action, at which point Quirrell would have had to pause what he was doing in order to intimidate Harry into compliance (and wait for him to deal with the shock etc.).
Quirrell sometimes makes the mistake of pushing people too much. Perhaps as a consequence of too much cynicism. Harry would probably help Quirrell just because he cares about him… but Quirrell does not understand the concept of “care” and thinks it is only a role that Harry feels obliged to play, which he does not trust as a sufficient motivation to overcome obstacles. So he add further motivation; things that seem sufficiently motivating in his model of Harry.
While Quirrell could have asked Harry to help him as a friend, it would have risked Harry balking at any step in the process which involved sufficiently unethical action, at which point Quirrell would have had to pause what he was doing in order to intimidate Harry into compliance (and wait for him to deal with the shock etc.).
Quirrell sometimes makes the mistake of pushing people too much. Perhaps as a consequence of too much cynicism. Harry would probably help Quirrell just because he cares about him… but Quirrell does not understand the concept of “care” and thinks it is only a role that Harry feels obliged to play, which he does not trust as a sufficient motivation to overcome obstacles. So he add further motivation; things that seem sufficiently motivating in his model of Harry.