Penal substitution is a theory of the atonement within Christian theology, especially associated with the Reformed tradition. It argues that Christ, by his own sacrificial choice, was punished (penalised) in the place of sinners (substitution), thus satisfying the demands of justice so God can justly forgive the sins.
#9 It makes God look mean and angry
Was God's wrath directed towards Jesus instead of towards us? Did God the Father punish Jesus instead of me?
Is God not capable of loving sinners? Does God hate sinners?
Does God ever quit loving us? Did God stop loving Jesus when he was on the cross?
I'm OK with a loving father disciplining his children - but can killing ever be done in love?
The description of a Jesus who paid our debt makes Jesus look like a good guy. But it also makes God the Father out to be a God who requires human sacrifices to appease him (either ours or Christ's).
#8 It gets told over and over again in some evangelical churches
#7 I don't think bearing our burden means punished by God instead of me
The phrase "bearing our burden" is in Scripture but see this post for more on this.
#6 Contrary to popular belief, the Mosaic sacrifices did not operate in a Penal Substitution framework.
See this post for more on this.
#5 You won't find the phrase Penal Substitutionary Atonement in Scripture
#4 You won't find the phrase "Jesus Paid our debt" in Scripture
Scripture uses the word ransom, which I think is different. When you pay a ransom you are paying money to a bad or evil force who has held someone captive. Is God the bad evil force that needed to be paid? Or is it our selfishness/sin?
#3 You won't find the phrase "Jesus paid the penalty of man's sin" in Scripture
#2 Some people think Penal Substitutionary Atonement is the gospel
#1 The gospel that Jesus preached over and over again was about the good news of the kingdom of God.
There may be some truths in the Penal Substitutionary Atonement theory. The work that Jesus did on the cross is a beautiful and complex mystery. But I don't think this theory deserves the emphasis it often gets.