So, why should His disciples not aspire to 'always be right'?   

They should.   

The problem with 'always being right' is when you don't allow others to be wrong (or at least differ with us).   

God allows us to be wrong and so we should allow others to be wrong.   

But God identifies error and so should we.   
The key is keeping our notion of 'right' connected with His Word.   

Preach the word; be instant in season, out of season; reprove, rebuke, exhort with all longsuffering and doctrine. 2Ti 4:2 This is the order of the day to all believers.     We are to:    ➛ publicly proclaim the Gospel.         ➛ be ready to share the Truth    ➛ reprimand and censure those who sin    ➛ express strong disapproval of evil    ➛ strongly encourage people to receive Christ    ➛ stay within the authority of the scriptures with these actions    ➛ not harangue individuals with the Gospel    ➛ make sure everyone we know hears it from us.