Comparing nearly identical expressions

I will attempt to prove that $\infty- \infty =2$ . In which of the 3 steps below did I first make a mistake by using flawed logic?

• Step 1: Consider the two expressions $(1 + 2 + 3 + 4 + \cdots)$ and $(1 - 2 - 3 - 4 - \cdots).$
• Step 2: If we were to add up these two, all but the first numbers are canceled out in pairs: $\begin{aligned} &(1 + 2 + 3 + 4 + \cdots) + (1 - 2 - 3 - 4 - \cdots) \\\\ =& (1 + 1) + (2-2) + (3-3) + (4-4)+ \cdots \\\\ =& 2 + 0 + 0 + 0 +\cdots. \end{aligned}$
• Step 3: Simplifying this equation gives $\infty - \infty = 2 .$