I’d suspect that the settings in your sendmail.cf are incorrect. It could possibly also be due to the version of openssl you have installed on that server.
# CA directory
O CACertPath=/etc/ssl
# CA file
O CACertFile=/etc/ssl/intermediate.ca
# Server Cert
O ServerCertFile=/etc/ssl/woolspire.crt
# Server private key
O ServerKeyFile=/etc/ssl/woolspire.key
# Client Cert
#O ClientCertFile=/etc/ssl/woolspire.crt
# Client private key
O ClientKeyFile=/etc/ssl/woolspire.crt
# File containing certificate revocation lists
#O CRLFile
# DHParameters (only required if DSA/DH is used)
#O DHParameters
# Random data source (required for systems without /dev/urandom under OpenSSL)
#O RandFile
This strikes me as strange - are you 100% sure you want to be configuring mutually authenticated TLS with a ClientKeyFile? If so I'd also expect to see the ClientCertFile uncommented. For a mailserver intended to send mail to other Internet mailservers I wouldn't expect you to need a client certificate or key to send outbound STARTTLS mail at all. Maybe you could try commenting out the ClientKeyFile line and trying again?
Edit: This is definitely the problem I read more carefully and you're using the .crt file as the ClientKeyFile. As expected sendmail balks at using a certificate as a private key for client authentication.