–Beliefs must be Justified–
The Egoist who obtains the ability to be persuaded by sufficient reason must accept beliefs should be justified. Debate itself, regardless if involved in ethics or otherwise, implies beliefs require interpersonal justification, as all debate is to reason about beliefs.
 

–Rejection of Justification forfeits all Argument–
To reject the idea that beliefs require justification, is to forfeit all argumentative force, to fully reject all ability to make claims others have any sufficient reason to accept, and to grant yourself the ability to take up any position without justification.

For an Egoist to take up this position is to fall for the Igism dilemma. If an Egoist attempts this you may simply respond claiming to be a believer of Igism, where Igism is the idea that one should say 'Ig' once a day, and encourage others to do the same, while attempting to form a coercive government that indoctrinates others into Igism.

For an Egoist to reject debate is for them to grant Igism equal weight to their own framework. Any objection to the claim that beliefs should face justification is also to object to the very argumentative force of the objection itself, since a belief in the objection or acceptance of it's conclusion itself counts as a belief and suddenly cannot be justified in a way binding to any agent.
 

–What is a Belief?–
What is a belief, though? Ultimately a belief is something you act on, a conclusion you accept and would bet on being correct, and may guide your actions. In a physical sense you can think of it as a pattern within your own brain.

Acceptance of beliefs based on justification can then be thought of as internal actions, as actions you take within your own mind.
 

–Actions require Followed Beliefs which face Justification–
In-order for Justification Ethics to work, we must derive the claim that actions should be justified normatively in the first place. How can this be shown? Well, this is in effect asking how the justificatory burden of internal actions should imply a justificatory burden on external actions.

This can be shown by realizing some beliefs are followed in the present moment and guide action. If you take an action, it can be said that an internal action guided your mind which caused the action to happen, as actions are the output of a mind.

We can call such beliefs, "followed beliefs". These followed beliefs, as beliefs, have justificatory burden, thus the beliefs that lead to actions against others must require justification.
To reject this is to forfeit all argument as explained earlier.

For intentional actions, the actions performed as a consequence of these followed beliefs, a justificatory burden placed on the agent who performed the action is directly implied by the followed belief, as beliefs require justification.
 

–Justification Ethics–
If someone is to attack another person, that is an action performed as a consequence of a followed belief. That action being taken implies the existence of the followed belief being accepted by the agent in some form, and that belief requires justification.

If said belief cannot be justified, then an action that cannot be normatively justified implies a failure of reason in the sense of the presense of unjustified beliefs.
Thus, such intentional actions imply a justificatory burden. This is the fundamental premise of Justification Ethics, which then derives Interests as a value.


–Actions Must be Justifiable - Deductively Proven–
–Definitions:
(Belief): A proposition accepted as true by an agent.
(Followed Belief): A belief, principle, or judgement that an agent is presently acting according to.
(Interpersonal Justification): A deductive argument that derives the conclusion that another rational agent ought to accept some belief from premises they are rationally required to accept.
(Intentional Action): An action intentionally performed according to one or more followed beliefs.

–Premises:
(P1): Acceptance of any rational deductive argument presupposes that beliefs presented as reasons for action or acceptance of claims, require interpersonal justification.
(P2): Intentional actions are performed according to one or more followed beliefs.
(P3): If an action is performed according to a followed belief that possesses a justificatory burden, then the action inherits a justificatory burden from that belief.

–Logic:
(L1): From (P1 + P2), intentional actions performed according to beliefs presented as reasons are performed according to beliefs that require justification.
(L2): From (P3), an intentional action derives its justificatory burden from the followed belief according to which it is performed.

–Conclusion:
From (L1 + L2): Therefore, intentional actions performed according to followed beliefs presented as reasons, are thus actions subject to interpersonal justification.

Thus, certain actions do require justification, the fundamental premise of Justification Ethics.
To reject this conclusion, is to forfeit the rational force of one's own objection, since an objection is itself an attempt to justify the acceptance of a belief by appeal to reasons.