Kazhdan himself proved in his 1967 paper (where he introduced property (T)) that simple Lie groups $G$ of real rank $\textrm{rk}_{\mathbf{R}}(G) \geq 2$ have the property (T). This fact can be proven by different methods, e.g. (like in Bekka-de la Harpe-Valette) by proving the corresponding fact for $\textrm{SL}_3$ and $\textrm{Sp}_4$ and reducing the general case to these groups, or alternatively, by proving a relative property (T) for the pair $(\textrm{SL}_2(\mathbf{R}) \ltimes \mathbf{R}^2, \mathbf{R}^2)$ and reducing the general case similarly.
I am also familiar that the complementary series $(\pi_{\lambda})_{-1 < \lambda < 0}$ show that $\textrm{SL}_2(\mathbf{R})$ does not have property (T). I am wondering whether there is a conceptual reason (along the lines of rank 1 groups have insufficient directions) why property (T) cannot be proven for rank $1$ like in higher rank, and how to formalize this conceptual reason. I know that this is a very imprecise question, and I would be really happy with any intuitions.
Thank you very much in advance!
