The simplest answer is that the legislation authorizing the Twain commemorative program did not include a half dollar coin in its "Coin Specifications" section. When it comes to modern US commemorative coins, the US Mint can only strike what is authorized by Congress and the President.
Note: The Mint does have some leeway in terms of creating special edition "collector packages" to supplement the standard coin releases. These special edition sets are not specified in the coin's legislation but can be created by the Mint as long as the commemorative coin they include has been authorized and that the coins used for the sets are taken from the overall authorized mintage.
Getting back to the Twain coins.
Though passed in the 112th Congress in 2012, bills calling for a Twain commemorative program date back to 2008 and the 110th Congress; bills were also introduced in the 111th Congress. None of the bills introduced included a request for a half dollar coin.
The sponsors of a commemorative coin program generally drive the request that gets proposed by their Senator or Representative. Before a bill is introduced, there are meetings between representatives of the sponsor and the Senator/Representative that will put the bill before Congress. A discussion of what would give the bill the best chance of gaining support and being passed ensues.
If you look at the recent history of the US commemorative program, there isn't a set pattern as to what proposals get introduced in Congress or what gets approved and sent to the President for signature. There have been a number of programs that requested a single silver dollar alongside those that sought clad, silver and gold coins.
As I noted above, sponsors are part of the decision process that determines what gets introduced. In the case of the Twain program, it would appear that the sponsor was OK with having a precious-metals-only program - they had many opportunities to request a half dollar be added to their bill, but no addition was ever made.
One potential drawback to having a half dollar as part of a program is that it could siphon surcharges away from the sponsoring organization. By this I mean, each sale of a clad half dollar coin generates a $2 or $3 surcharge while the sale of a silver dollar generates $10. Thus, it takes the sale of more than three clad half dollars to generate the same surcharge revenue for a sponsor as one silver dollar.
A sponsor may feel that too many silver dollar sales would be lost if a lower cost option was made available, and that the net result would be a lower overall surcharge collection. If you look at recent program mintages, you'll find that sales of clad half dollars do not come close to tripling the sales of silver dollars. In fact, half dollar sales in some program have been less than those of the silver dollars.
Personally, I think the Twain program could have successfully supported a clad half dollar. Many younger collectors have likely recently read (or are about to read) one or more of Twain's books - this creates a natural link to the coins. A Twain half dollar would have been an ideal coin to include in a Young Collectors set for new collectors (and me!).
Hope that helps answer your question.
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