To explain why a negative sloping yield curve is bad, you have to start with a theory of the yield curve.
The dominant theories for the term structure of interest rates are the rational expectations, liquidity preference, and market segmentation. (The first two theories are quite compatible with each other and have more standing so let's assume that view.)
Generally, we expect longer-term maturities to have correspondingly higher yields because the investor must bear more risk (inflation risk, bond price risk, interest rate risk, liquidity risk, credit risk). So it is indeed "abnormal" to observe an inverted yield curve -- why would an investor hold longer-term maturities in the face of these risks? The answer is that that long-term investors expect the term-structure of rates to drop even further. These expectations can be measured in the implied forward rates of the term structure.
What is the negative slope mean for economic growth? The negatively sloped yield curve is a function of the short-rate and longer-rates. The Federal Reserve targets the short-rate thru open market operations (purchases and sales of short-term treasury bills). The Fed may raise the short-rate substantially to limit credit growth.
In this world, bank have less incentive to lend long and fund capital or residential investment projects since banks can lend short and capture a higher rate. This reduces the pace of credit growth and the number of new projects financed by debt. Also, the risk-free rate is an asset class that competes with equities and other asset classes (housing, gold, etc.). The higher the short-term rate the less speculation in other asset classes which can lead to bubbles bursting.
Note that banks will still continue to issue loans at longer maturities, however, they will focus on higher quality investment-grade credits. Firms that have marginal access to credit may experience re-financing difficulties and may not benefit from lower long-term risk free rates since credit spreads typically widen in a recession.
Also, there is research showing that long-term treasury rate is a proxy for nominal economic growth. If the long-rates are very low and the short-rate is high, the bond market is anticipating weak economic growth and future Fed rate cuts.