I employed close-reading, which was a part of the training I received in graduate school earning my Masters in English and is a technique all literary critic use to carefully analyze and understand a text.
This may involve:
1)
closely looking at details and how specific words are being used: such as my pointing out that the text shows God is inciting David to perform a census out of
anger with Israel. It says so explicitly.
2)
Considering how a character is being portrayed and their motivation from those details: God leads David to perform a census out of anger. God's motivation is anger.
3)
Identifying patterns:
a) God incites David to perform a census from anger
b) Joab's response to David suggests that he is doing something wrong or highly unusual ("but why doth my lord the king delight in this thing?" - KJV, "But why does my lord the king want to do such a thing?” - NIV)
c) after the census, David's conscience leads him to explicitly declare that he sinned by having performed the census ("And David’s heart smote him after he had numbered the people. And David said unto the LORD, I have sinned greatly in having done this; but now, I beseech thee, O LORD, take away the iniquity of thy slave, for I have done very foolishly." - KJV)
d) Chronicles reassigns the blame for this census from God to Satan (literally from the good guy to the bad guy, at least from a Christian perspective).
Conclusion: If you look at each element of the pattern, the text is implying that census taking of this sort is a sin.
4)
Situate an analysis in previous scholarship and larger themes of a writer:
The Documentary Hypothesis is a well accepted scholarly theory in Biblical and literary studies. It suggests the bible had multiple writers. The evidence for this tends to be linguistic and thematic. One of those writers was the Deuteronomist. The Deuteronomist style is didactic and moralistic. They are the writers behind the semi-"historical" narratives (Joshua, Judges, Samuel, and Kings). Their authorial standpoint is to look back on history and try to explain disastrous events in terms of Israel or the leaderships' failure to follow God's rules. So this gives us some context of what the writers might be thinking in terms of why a King-ordered census is a sin. It seems that it is a sin because the Deuteronomist perceives something secular and disobedient to God's covenant in this census taking of military men. This reading is supported by the textual detail where David claims after repenting for taking the census and having to decide on his punishment that he'd rather put his faith in God for his punishment than the hands of men. So we see the writer emphasizing putting one's faith in God over humanity, pretty typical for the Deuteronomist.
Interestingly, Exodus 30:11-12 states - "Then the Lord said to Moses, “When you take a census of the Israelites to count them, each one must pay the Lord a ransom for his life at the time he is counted. Then no plague will come on them when you number them." So another possibility is as simple as them not paying the ransom money required during a census.
If there was something that didn't make sense to you, I would be happy to explain further. No need for the ad hominem attacks if you disagree. I just assumed you wanted to have a literary discussion as we're on a literature forum, which implies that we ought to use literary methods.