Even when it seems like baby is interested in food before then, often they're just interested in mimicking you, and would copy you putting something in your mouth the same way they'd copy putting your hairbrush on your head -- just copying, not intestinal lining cellular changes, the thing we're really waiting for.
There are very good reasons to delay solids until at least 6 months ...
1. It's recommended by the World Health Organization, UNICEF, The American Academy of Family Physicians, National Health & Medical Research Council, and many prominent pediatricians. The lower range numbers, and many of the reasons along with it, have been outdated for quite awhile.
2. Waiting until the cells lining the baby's gut have closed helps prevent many allergies, gas, rashes, and medical issues.
3. Waiting also shows less incidences of gastroenteritis, diabetes, and obesity (as much as six-fold!) and even ear infections.
4. Breastfeeding for at least seven months actually shows decreased rates of anemia.
5. Baby is much less likely to choke -- even on purees -- when baby is older, and can also sit upright of their own accord (babies should never be fed foods leaning back).
6. Baby's gut doesn't produce enzymes to aid in digestion until 3-4 months, and the ones that break down more complicated fats, starches, and carbohydrates won't be produced until 6-9 months, meaning lots of gas, constipation, vomiting, and wasted nutrients before then. Even generally fussiness months later is noted in babies who were started too early.
7. While some babies may be ready between 4-6 months (no evidence has ever shown anything but risks earlier), it's impossible to tell without looking with a microscope in the gut, so waiting until 6 months minimum is a safer move for all babies.
8. Waiting until your baby can pick up and put food into their own mouth while sitting up straight is a clear sign of readiness, especially if they can gum and swallow the foods. The Department of Health's Infant Feeding recommendation actually suggests allowing babies who show readiness before 6 months to play with finger foods (that's right, no purees), as it's also unlikely they will swallow before they're biologically ready.
9. The tongue thrust reflex is to help prevent choking, but spoons of liquid purees can often get past it, since the reflex point is farther forward than an adult's gagging reflex. Putting food in the front of the mouth and allowing baby to move it back, which they can't do until often after 6 months, helps prevent choking and is also, of course, a sign of readiness.
10. Most parent assumptions about when babies are ready are related to other biological norms -- waking up at night, reaching for food, mimicking your eating, wanting to eat more -- and are confused for signs of readiness. Having a set date AND a list of readiness signs helps prevent early introduction based on confusion about normal behaviors.
My friend at the Analytical Armadillo has a much longer and science-heavy post that I adore, but after all is said and done, it pretty much comes down to this: There are no benefits, only risks, to starting a baby before they're biologically ready, and since we can't see the gut, we have to go by outside cues, and waiting until a bare minimum of 6 months is the safest way to play it. If a couple weeks is the difference between a gut infection and not, the choice is pretty clear.