I would guess that you are running logstash as a service and whatever service manager you are using is cc'ing stdout to /var/log/syslog. You can reconfigure that in the service manager.
[Unit]
Description=logstash
[Service]
Type=simple
User=logstash
Group=logstash
# Load env vars from /etc/default/ and /etc/sysconfig/ if they exist.
# Prefixing the path with '-' makes it try to load, but if the file doesn't
# exist, it continues onward.
EnvironmentFile=-/etc/default/logstash
EnvironmentFile=-/etc/sysconfig/logstash
ExecStart=/usr/share/logstash/bin/logstash "--path.settings" "/etc/logstash"
Restart=always
WorkingDirectory=/
Nice=19
LimitNOFILE=16384
[Install]
WantedBy=multi-user.target
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