why doesn't java send the client certificate during SSL handshake?

It's possible that you may have imported the intermediate CA certificate into the keystore without associating it with the entry where you have your client certificate and its private key. You should be able to see this using keytool -v -list -keystore store.jks. If you only get one certificate per alias entry, they're not together.

You would need to import your certificate and its chain together into the keystore alias that has your private key.

To find out which keystore alias has the private key, use keytool -list -keystore store.jks (I'm assuming JKS store type here). This will tell you something like this:

Your keystore contains 1 entry

myalias, Feb 15, 2012, PrivateKeyEntry, 
Certificate fingerprint (MD5): xxxxxxxx

Here, the alias is myalias. If you use -v in addition to this, you should see Alias Name: myalias.

If you don't have it separately already, export your client certificate from the keystore:

keytool -exportcert -rfc -file clientcert.pem -keystore store.jks -alias myalias

This should give you a PEM file.

Using a text editor (or cat), prepare file (let's call it bundle.pem) with that client certificate and the intermediate CA certificate (and possibly the root CA certificate itself if you want), so that the client-certificate is at the beginning and its issuer cert is just under.

This should look like:

-----BEGIN CERTIFICATE-----
MIICajCCAdOgAwIBAgIBAjANBgkqhkiG9w0BAQUFADA7MQswCQYDVQQGEwJVSzEa
....
-----END CERTIFICATE-----
-----BEGIN CERTIFICATE-----
MIICkjCCAfugAwIBAgIJAKm5bDEMxZd7MA0GCSqGSIb3DQEBBQUAMDsxCzAJBgNV
....
-----END CERTIFICATE-----

Now, import this bundle back together into the alias where your private key is:

keytool -importcert -keystore store.jks -alias myalias -file bundle.pem

As an add here, you can use %> openssl s_client -connect host.example.com:443 and see the dump and check that all the main cert is valid against the client. You are looking for this at the bottom of the output. Verify return code: 0 (ok)

If you add -showcerts it will dump all the info of the keychain that was sent along with the host certificate, which is what you loaded into your keychain.