How would you respond to a critic who says that God is a moral monster because of the commands to kill the Canaanites?
I do appreciate your question because it is a very good one: hard to wrestle with and considers a lot of reflection. Since, of course, I have readers who pass through these questions I wanna give a quick introduction to the severity of the issue (Section I), and the following section(s) can be a possible response to the subject (Section II).
I always try to set up my writing in different sections, while however keeping each section mutually exclusive but not totally irrelevant to each other. So, as I always say, if you would like to skip to the answer, then you are more than welcome to skip to Section II whereas I will only provide some brief introduction simply there for your prerogative to read.
The Command to Kill the Canaanites
Probably the most gripping passage regarding God’s command and the Canaanite’s can be found Deuteronomy 20, where Moses records:
However, in the cities of the nations the Lord your God is giving you as an inheritance, do not leave alive anything that breathes. Completely destroy them – the Hittites, Amorites, Canaanites, Perizzites, Hivites and Jebusites – as the Lord your God has commanded you. Otherwise, they will teach you to follow all the detestable things they do in worshiping their gods, and you will sin against the Lord your God. (Deut. 20:16-18; NIV)
Genocide simply defined means “the systematic extermination of an entire national group” . This is surely a much troubling circumstance of Old Testament history for theologians and commentators alike. John Calvin even notably wrote that “the decree is dreadful indeed, I confess” . More so, Andy Woods (2005) in his paper on the genocide of the Canaanites, recognizes that
[m]ore significant than embarrassment for the theologian, biblical genocide has proven to be a stumbling block preventing people from trusting Christ as savior. Many rationalize that the God of the Bible is no more humane than the God of Islam on account of the fact that divinely sanctioned genocide is found in the major holy books of both religions. Thus, an explanation of biblical genocide has become a key Christian apologetic issue of our day. 
It must first be noted that in verses 10-15 God is directing His people on how to deal with the cities they’ve made war with. In verse 10 we see, “[w]hen you march up to attack a city, make its people an offer of peace” (Deut. 20:10; NIV). God continues up to verse 12 in explaining what to do when (1) the city “opens their gates” and (2) when the city refuses to make peace. For (1):
- (1) “[A]ll the people in it shall be subject to forced labor and shall work for you.” (v. 11)
- (2) “[L]ay siege to that city.” (v. 12)
- (2’) Verse 13 continues: “When the Lord your God delivers it into your hand, put to the sword all the men in it. As for the women, the children, the livestock and everything else in the city, you may take these as plunder for yourselves.”
Thus, Matthew Henry (1662-1714) in his Commentary writes in respect to these passages:
Even to the proclamation of war must be subjoined a tender of peace, if they would accept it upon reasonable terms. They must first proclaim peace to them. Let this show: (1) God’s grace in dealing with sinners: though he might most justly and easily destroy them, yet, having no pleasure in their ruin, he proclaims peace, and beseeches them to be reconciled.
(2) Let it show us our duty in dealing with our brethren: if any quarrel happen, let us not only be ready to hearken to the proposals of peace, but forward to make such proposals. We should never make use of the law till we have first tried to accommodate matters in variance amicably, and without expense and vexation. We must be for peace, whoever are for war. 
However, the Canaanites as recognized by Henry “are excepted from the merciful provisions made by this law.” By “this law,” Henry means the provisions as seen in verses 10-12; the nations of Canaan were ordered to simply be destroyed in light of their idolatry and destruction .
Some Reflections on the Canaanites
In addressing the issue of just exactly how “wicked” were the Canaanites, philosopher from West Palm Beach Atlantic University Paul Copan in his Is God a Moral Monster? writes:
What kind of wickedness are we talking about? We’re familiar with the line, “The apple doesn’t fall far from the tree.” In the case of the Canaanites, the Canaanites’ moral apples didn’t fall far from the tree of their pantheon of immoral gods and goddesses. So if the Canaanite deities engaged in incest, then it’s not surprising that incest wasn’t treated as a serious moral wrong among the Canaanite people. [ … ] adultery (temple sex), bestiality, homosexual acts (also temple sex), and child sacrifice were also permitted (cf. Lev. 18:20-30). [ … ]
Let’s add to this the bloodlust and violence to the Canaanite deities. Anath, the patroness of both sex and war, reminds us of the bloodthirsty goddess Kali of Hinduism, who drank her victims’ blood and sat surrounded by corpses; she is commonly depicted with a garland of skulls around her neck. 
Copan goes on to comment that Canaanite idolatry was so intertwined with Canaanite society, that “it’s no wonder God didn’t want the Israelites to associate with the Canaanites and be led astray from obedience to the one true God” . However,
I’m not arguing that the Canaanites were the worst, specimens of humanity that ever existed, nor am I arguing that the Canaanites won the immorality contest for worst-behaved peoples in all the ancient Near East. That said, the evidence for profound moral corruption was abundant. God considered them ripe for divine judgement, which would be carried out in keeping with God’s saving purposes in history. 
That being said, I think the thesis of Henry and Copan combined make a very interesting and respectively meaningful story – and not some capricious act of God; provoked by some feelings of “anger” or “jealousy” – of God’s grace and how he shows it towards sinners. The theological significance of the Canaan story carries with it the ultimate story of Grace.
-  Funk & Wagnalls Standard Desk Dictionary (Harper & Row: 1964) s.v. “genocide.”
-  John Calvin, Institutes of the Christian Religion, trans. by Henry Beveridge (Eerdmans, 1975) 3.23.7
-  Andy Woods, Canaanite Genocide (2005) p. 1 (PDF Available)
-  The Matthew Henry Commentary (Zondervan: 1961) p. 192
-  Henry continues on this point: “Care is here taken that in the besieging of cities there should not be any destruction made of fruit trees, v. 19, 20. The intent of the divine precepts is to restrain us from destroying that which is our life and food. Armies and their commanders are not allowed to make what desolation they please in the countries that are the seat of war. No fruit tree is to be destroyed unless it be barren, and cumber the ground” (Ibid., p. 192).
-  Paul Copan, Is God a Moral Monster? (Baker Books: 2011) p. 159
-  Ibid., p. 160
-  Ibid.