老板很nice，You noticed. It must have given a warm and fuzzy feeling. "Nice" is not a good thing here. His niceness left you to fend for yourself.
我是开发出身. Do not think this way. Ask if you were a manager, what you would say and do. Ask more why things are done than how it is done. If you don't, your coworker will fill the vacuum.
本来有分工，You don't know this for certain. You are telling yourself this to justify. Why do you need such justification?
需要时间熟悉东西. You need to actively think/know what it should look like, rather than passively find out what it is.
然后以手上活多为由, He is acting like your manager.
按道理， 他的垃圾活我是要会的, Why? You want to be nice and reasonable, to elicit the same in return. But it has been interpreted as weakness.
以备他休假时我可以做backup, Even if it is true, he shouldn't know you readily accept this. This was his openning to dump on you.
我很不擅长和别人争执, Smile that business grin. You do not need a long face to justify your issue. You are worthy just by your very being. Value yourself, because no one else is going to do it for you. Focus on the issue, which is not part of you. Say to yourself: this is unpleasant, but so what. Do not let your "flight" response distract you.
除非他休假, You don't need this conditional. Next time you want to say "I'm a reasonable guy", don't! Do not let reason as the reference point, you are the reference point. You alone are reason enough.
我就火上头, Think of your childhood, when you got mad, what was that event? Is your present response a reflex left over from that long-ago time? Is such reflex still suitable for today?
有理有据的回复, You are looking for a third reference point outside of you. Seeking such a point tells the other guy that you don't think much of yourself.
