Society and community
Royce talks of 'society' in your quotations but his key idea is that of 'community'. It is on the relation between the individual and the community that his social and political theory turns. 'The Philosophy of Loyalty' (1908) concerns loyalty of the individual to the communuity' and the theme of community as the central social and political concept is set out in 'The Sources of Religious Insight', chap. 5, and promoted in 'The Problem of Christianity' (1913) - hereafter 'PC'.
Someone might say that in framing my answer in terms of 'community' I am failing to answer your question. But I really am not. Royce's focal interest is in the form of society that he terms 'community'. This is apparent when one moves beyond isolated quotations.
In his own attempt to explicate the general term "community,"
Royce considers three conditions requisite for its existence. The
first is an integrated individuality, or rather two or more such
integrated individualities. Community is founded upon "the power
of an individual self to extend his life, in ideal fashion, so as to
regard it as including past and future events which lie far away
in time, and which he does not now personally remember." [PC 11 (New York, 1913.] Each
self is the present reality of a particular past and a particular future, the interpreter of what has been and will be in his own unique
regard. It is from his own unrepeatable individuality that a man
contributes to the greater wealth that is community.
The second condition for ... community is communication
among the various selves. This is not something that happens automatically, for "a community does not become one ... by virtue
of any reduction or melting of these various selves into a single
merely present self, or into a mass of passing experience." [PC: 67.] Rather
the existence of community depends upon the fact that there are
in the social world a number of distinct selves who are not only
capable of social communication, but also generally engaged in
The last requisite is a principle of unity through which the individuals involved share a common past and/or a common future.
In regard to their past, the group constitutes a community of
memory; in regard to the future, a community of hope. To Royce,
[t]his third condition is the one which furnishes both [sic] the
most exact, the most widely variable, and the most important
of the motives which warrant us in calling a community a real
unit. [PC: 68, 69.]
Insofar as they are conscious of their unity, the members are empowered to act as a community as well as individuals. In so acting
they achieve a personal reality over and above their isolated individualities.
Collecting the conditions stipulated for genuine community we
can formulate the following general Roycean definition: community
is a reality constituted by unique individual selves who share a common history and/or aim. All the instances of community which
Royce describes in some way fit this definition. None fits it so well,
however, as the Universal or Beloved Community, the ideal to
which all other communities can only approximate. (M. L. Briody, 'Community in Royce: An Interpretation', Transactions of the Charles S. Peirce Society, Vol. 5, No. 4 (Fall, 1969), pp. 224-242: 225-6.)
"The tension between the individual and society is teaching men customs, equipping them with tools for expressing their own personalities. Society constantly engaged in training up children who may, and often do, rebel against their mother."
'Rebel' is somewhat vague and imprecise. One reading is that each member's 'unrepeatable individuality' introduces novelty into the community. One individual never assimilates a custom in exactly the same way as others do - and may, and often does, modify and amend it. This idea needs elaboration if it is to do much work, however.
On your main point, concerning the alignment of individual best interest with communal best interest, my only comment is that a community's 'best interest' appears to Royce to be that of becoming a Universal or Beloved Community; and that the individual's 'best interest' is to be a member of such a community. This requires fulfilment of the three conditions listed at the start.
Note on 'argument'
Conifold very rightly points out that in the passage you quote, Royce 'is not arguing for anything, he is just making an observation'. There is an increasing usage in which, when a philosopher makes a claim that p, s/he is said to 'argue that p'. To argue is to draw a conclusion from premises. This usage collapses all depth out of 'argument' and 'arguing'.