As per your question it seems you are using broad leaf dicot plant leaf for the DNA isolation. For the DNA extraction it is preferred to use the fresh and new tissue for easier and quality DNA extract. The main purpose of avoiding large veins is the complete grinding and homogenization of the tissue. Large veins could hamper the homogenization. Additionally, a minor effect of the veins could also be the presence of comparatively higher plant metabolites/secondary metabolite or other specialized chemical could possibly effect the quality of DNA (rarely seen in daily lab practice).
I agree with Abhijeet. We remove the main veins in plant leaves due to them being tough to lyse compared to the young leaf blade tissue. The components of plant vascular tissue (cellulose, for example) contribute to more cellular debris that can cause harm to your high-molecular weight DNA, especially of you use physical disruption such as maceration or bead beating.
the large plant veins contain high amount of polysaccharide, which may interfere and hamper the dna isolation process and may give you low yield, hence it should not be present.
We have to remove the large veins because these parts do not have much DNA to be extracted and grinding process will be hampered because it is very solid and stubborn, also it contains a large quantities of contaminants (salts and phenols).