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It is not just the loss of rare breed animals that should concern us.
Since the 1980s it is estimated that we have lost 95% of agricultural diversity ~ man's common heritage.
We are increasing reliant on just a few strains of wheat, corn and rice, for all our global needs.
Resistance in pests and diseases is increasing and requires constant development for the seed companies to stay ahead in the arms race.
With only a few varieties, if a crop succumbs to pests or disease, the whole harvest can potentially be lost with catastrophic results.
Local varieties were adapted to local conditions, and had wide genetic variance, providing a safety net against total loss of a nations harvest.
Remember the potato famine in Ireland? The whole crop got blight, leading to mass starvation.

As varieties are bred for certain characteristics, such as yield, or short stalk length, other traits, such as hardiness, resilience or resistance are lost, and the genetic diversity declines.

Before seed giants (like Monsanto) engineered rice, native strains would grow in the paddies, using inputs from buffalo dung and with nitrogen fixed from the blue-green algae. Modern engineered varieties will not grow without inputs of fertilizer which must be purchased, something the poor can ill afford, and which has negative environmental consequences.

In addition, among the latest developments are suicide seeds, which are sterile, and cannot be saved by the farmer to be planted the following year; and varieties containing patented genetic markers, which you must pay to grow. These developments have the potential continue to current trend and place a few hugely powerful seed companies in complete control of all global production.
How will the worlds poor, dependent upon subsistence farming (at least those not already dispossessed), with no money to buy expensive seed or artificial fertilizer feed themselves?
Most of these commodities are produced and exported by only 6 countries, and most (close to 80%) of the world's trade in these commodities is held by a handful of corporate agribusiness, who control the global market and whose primary aim is their profits.

Prior to 1945, most of the worlds countries were self sufficient, now thanks to trade liberalization, globalization and the economic miracle it promised, the world's poorest countries are dependent upon imports for their food, and at the mercy of agricultural productivity (or failure), and trade policies half a world way, faced with rocketing prices as deregulation of the market has encouraged speculation.

Food is a basic need for life, it is a basic right, it is not a commodity, and is far to important to leave to global corporations and global market forces. Local produce, local solutions, food security and food sovereignty are solutions to the growing global crisis.

Predictions that we can feed a growing population are based upon continuation of the colossal yield growths we saw in the green revolution. This is not realistic, yield growth has dramatically declined, and we cannot rely that there will be a miracle of technology to save us. Or if there is that it will be appropriate and sustainable.

Technology has allowed human society to transcend the factors which impose limits on other species on earth. Resources are not infinite - a radical shift in attitudes and behaviour is required if we are not to transcend the carrying capacity of the earth.