Offer

v.kind, hopefulwarm

What it means

To present help, an idea, or an opportunity for someone to accept.

Reach for it when describing help, value, or opportunity presented for another person to choose

The community center will offer free evening classes.

everyday
give
when acceptance is assumed and plain language is enough
not when Give removes the recipient's choice and can imply transfer already occurred.
everyday
suggest
when a possible idea is shared lightly
not when Suggestion is weaker and less committal than offering action or resources.
warm
volunteer
when help is initiated without being asked
not when Volunteer normally applies to one's own time or service, not any offering.
professional
make available
when access is the practical result
not when Availability does not show that anyone personally offered it.
professional
present
when something is formally placed before an audience
not when Presentation does not necessarily leave a real choice to accept.
professional
propose
when an idea or course is put forward for consideration
not when Propose fits plans and terms, not a cup of tea or practical help.
professional
provide
when delivery rather than choice is central
not when Provide implies the recipient receives it, while an offer can be declined.
formal
extend
when courtesy, welcome, or an invitation is ceremonially given
not when Extend is formal and unnatural for most objects or services.

offer help
Several neighbors came forward to offer help after the storm.
offer an option
The clinic will offer an option that avoids weekday travel.
offer guidance
Mentors offer guidance without making the decision for the student.

The definition and the example on this page are written here. The dictionaries above ground which meaning is being described, not the wording.