why Chrome browser doesn't recognize my nginx http2 server?

Solution 1:

As per my answer on StackOverflow:

Will likely be one of two reasons:

1. You are using anti-virus software and it is MITM your traffic and so downgrading you to HTTP/1.1. Turn off https traffic monitoring on your AV to connect directly to the server.

2. You are using older TLS ciphers and specifically one that Chrome disallows for HTTP/2 (https://http2.github.io/http2-spec/#BadCipherSuites) as per Step 5 of above guide. Scan your site using https://www.ssllabs.com/ssltest/ to check your TLS config and improve it.

The third reason is lack of ALPN support in your SSL/TLS library (i.e. You are using openssl 1.0.1 and need to be one 1.0.2 or later, for example) but you have already confirmed you have ALPN support so skipping that for this answer.