We should not only exercise faith ( Hebrews 10:22) but also hope ( Hebrews 10:23) and love ( Hebrews 10:24). The admonition to hold fast to our hope is the one the writer emphasized most strongly in this epistle. It is an exhortation to perseverance. The basis of our steadfastness is the fact that God is faithful to His promises concerning our future. [source][source][source]
The third admonition ( Hebrews 10:24) moves from the vertical to the horizontal dimension of Christian living. This admonition to love one another, our social obligation, was also necessary since some were abandoning the faith. The readers needed to stimulate one another to remain faithful to the Lord. This type of love is the product of communal activity; we cannot practice it in isolation from other believers. [source][source][source]
"Any early Christian who attempted to live like a pious particle without the support of the community ran serious risks in an age when there was no public opinion to support him. His isolation, whatever its motive-fear, fastidiousness, self-conceit, or anything else-exposed him to the danger of losing his faith altogether." [1][source]
Regular attendance at church meetings facilitates love for one another because there we receive reminders and exhortations to persevere. It is only natural for one who has abandoned his faith to absent himself or herself from the meetings of his or her church. However this is the very thing such a person should not do. We need each other. [source][source][source]
"Whatever the motivation, the writer regarded the desertion of the communal meetings as utterly serious. It threatened the corporate life of the congregation and almost certainly was a prelude to apostasy on the part of those who were separating themselves from the assembly ..." [2][source]
The writer was urging mutual accountability since we will have to give an account of ourselves to God. The "day" that is approaching is the day we will give an account of ourselves to God (cf. Hebrews 10:37). This may have been an allusion to the destruction of Jerusalem in A.D70 for the original readers. [3] But it is definitely an allusion to the judgment seat of Christ. [source][source][source]