I’ve written plenty on this topic before, this is what I consider the strongest argument against inevitable perseverance/eternal security in a nutshell:
The primary purpose of a warning is to provide incentive to avoid its consequences.
A warning that can’t provide such incentive is effectively nullified in its purpose as a warning.
A warning can’t provide such incentive to a person who believes its consequences to be unrealistic.
A warning is therefore effectively nullified with regards to a person who believes its consequences to be unrealistic.
With that in mind,
The Bible sincerely warns believers against falling away from the faith and perishing.
The crux of the doctrine commonly called “perseverance of the saints” (and its variants, e.g. “eternal security”) is that no true believer can ever fall away to the point of perishing.
Because “perseverance of the saints” categorically denies that the consequences of the warning passages will ever be incurred by any saint, then the consequences of those warnings are unrealistic by such a view.
With regards to those who believe it then, the “perseverance of the saints” doctrine effectively nullifies the biblical warnings against believers committing apostasy.
 Consequences may be stated directly or implied, and avoidance can be in the form of positive and/or negative action; e.g. “Save for your retirement, or you’ll have insufficient funds.” or “Avoid running into traffic.”
 One could doubtless always find some other contrived purpose for a warning; it could be claimed that it’s being used to just get peoples’ attention through shock value, or perhaps inflate the length of a writing if nothing else! But the fact remains that if something keeps a genuine warning from instilling its hearers with some incentive to avoid what’s being warned against, then it is ultimately being rendered without force and ineffectual in its purpose.
 This should be self-evident. There may be warnings against things that a person could theoretically suffer, but some consequence that can’t be realistically incurred won’t give any reasonable person incentive to avoid it. Take for example the fact that quantum tunneling (theoretically anyway) allows for an almost infinitesimally small chance for solid objects to pass through each other: someone could warn me to stay in bed and not get up to reduce the chances of my falling through the floor. Such a warning wouldn’t deter me in the least from getting out of bed, because I know the chances of such an event actually happening are too absurdly low to be taken seriously.
 Going off the example ridiculous warning from , since I don’t believe I can realistically fall through a solid floor, for whatever other tertiary purposes such a warning might serve, it doesn’t give me any incentive to avoid its consequence, and is therefore ineffectual as a warning where I (along with anyone else who understands probability) am concerned. Regardless of how sincerely any warning is made, if one doesn’t believe it’s consequences are realistic, then to expect some caution or action on the part of that hearer to avoid said consequences is absurd.
 Matthew 5:27-30, 10:33, John 15:1-7, Hebrews 4:9-11, 12:15-17, Revelation 22:18-19, Romans 11:19-22, 2 Timothy 2:11-13 for just some examples. One could perhaps attempt to impute different meanings to the warning passages, asserting that they’re just idioms or some other literary device, but a rather heavy burden of proof would be on him to demonstrate from the context that the very apparent warnings against believers committing apostasy are something otherwise.
 Some proponents of these doctrines may concede that it’s possible in some sense for believers to fall away, but all are agreed that the scenario of a believer actually suffering such a consequence will without exception, never occur. While there is some variation in what proponents of eternal security believe, those details are irrelevant to this argument, as all versions of the doctrine teach that no saint will ever truly fall away.
 Note that this argument assumes someone interpreting warnings consistently with his beliefs.
 While eternal security proponents may attempt to sidestep the problem by appealing to the fact that unbelievers and false professors will perish, this argument concerns warnings directed specifically to the saints, not the unsaved.
One may also appeal to uncertainty, i.e. that one can’t know with absolute certainty that he’s saved, and so he likewise cannot be absolutely certain that he can’t suffer the consequence of damnation. That defense doesn’t exactly address the issue however, since acknowledging that one could conceivably be lost doesn’t change warnings against forfeiting one’s eternal inheritance into warnings against never obtaining said inheritance in the first place. Were the latter point the message being conveyed, we’d naturally expect the consequences to be framed in terms such as “you never were/aren’t grafted in,” rather than “you will be cut off.” All these defenses really do then is replace one problem (that of nullifying the scriptural warnings) with another (making the text out to say something it doesn’t indicate).